Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Cover of the book
Tytuł książki

Separation axioms, covering properties, and inverse limits generated by developable topological spaces

Seria
Rozprawy Matematyczne tom/nr w serii: 284 wydano: 1989
Zawartość
Warianty tytułu
Abstrakty
EN

CONTENTS
Introduction.............................................................................5
Notation..................................................................................8
§1. The spaces D and $D_1$................................................9
§2. D-completely regular spaces..........................................15
§3. On the epireflective hull of Moore spaces.......................24
§4. D-normal spaces.............................................................29
§5. D-paracompact spaces...................................................43
§6. Some characterizations of developable spaces..............55
§7. On inverse limits of developable spaces.........................62
References...........................................................................82
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 284
Liczba stron
88
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLXXXIV
Daty
wydano
1989
Twórcy
  • Rebhalde 7, D-7778 Markdorf/Baden, BRD
Bibliografia
  • Adamski, W., Complete spaces and zero-one measures, Manuscripta Math. 18 (1976) 343-352.
  • Aleksandrov, P. S., On the metrization of topological spaces. Bull. Acad. Pol. Sci. Sér. Sci. Math. 8 (1960) 135-140.
  • Aleksandrov, P. S. and Urysohn, P., Une condition nécessaire et suffisante pour qu'une classe (L) soit une classe (D), C. R. Acad. Sci. Paris Sér. I Math. 177 (1923) 1274-1276.
  • Alster, K. and Engelking, R., Subparacompactness and product spaces, Bull. Acad. Pol. Sci. Sér. Sci. Math. 20 (1972) 763-767.
  • Arkhangel'skii, A. V., Some metrization theorems, Uspehi Mat. Nauk 18 (1963) 139-145 (in Russian).
  • Arkhangel'skii, A. V., Functional tightness, Q-spaces and τ-embeddings. Comment. Math. Univ. Carolin. 24 (1983) 105-120.
  • Armentrout, S., A Moore space on which every real-valued continuous function is constant, Proc. Amer. Math. Soc. (1961) 106-109.
  • Bentley, H. L. and Herrlich, H., Completeness for nearness spaces, in: Topological Structures II, Part 1 (Proc. of the Symp. in Amsterdam, 1978), ed. by P. C. Baayen and J. van Mill, Math. Centre Tracts 115, Mathematisch Centrum Amsterdam (1979) 29-40.
  • Bing, R. H., Metrization of topological spaces, Canad. J. Math. 3 (1951) 175-186.
  • Blair, R. L., Closed-completeness in spaces with weak covering properties, in: Set-Theoretic Topology, ed. by G. M. Reed, Academic Press, New York (1977) 17-45.
  • Borges, C. R. and Gruenhage, G., Sup-characterization of stratifiable spaces, Pacific J. Math, 105 (1983) 279-284.
  • Brandenburg, H., Hüllenbildungen für die Klasse der entwickelbaren topologischen Räume, Dissertation, Freie Universität Berlin (1978).
  • Brandenburg, H., On ℰ-normal spaces, in: Categorical Topology (Proc. Int. Conf. Berlin, 1978) ed. by H. Herrlich and G. Preuß, Lecture Notes in Math. 719, Springer, Berlin, (1979) 24-34.
  • Brandenburg, H., On spaces with a $G_δ$-basis, Arch. Math. 35 (1980) 544-547.
  • Brandenburg, H., Some characterizations of developable spaces, Proc. Amer. Math. Soc. 80 (1980) 157-161.
  • Brandenburg, H., Separating closed sets by continuous mappings into developable spaces, Canad. J. Math. 33 (1981) 1420-1431.
  • Brandenburg, H., An extension theorem for D-normal spaces. Topology Appl. 15 (1983) 223-229.
  • Brandenburg, H., On D-paracompact spaces, Topology Appl. 20 (1985) 17-27.
  • Brandenburg, H., Upper semi-continuous characterizations of developable spaces, Math. Japon. 31 (1986) 185-196.
  • Brandenburg, H., On para-uniform nearness spaces and D-complete regularity. Acta Math. Acad. Sci. Hungar. 51 (1-2) (1988) 51-55.
  • Brandenburg, H. and Hušek, M., On mappings from products into developable spaces, Topology Appl. 26 (1987) 229-238.
  • Brandenburg, H. and Mysior, A., For every Hausdorff space Y there exists a non-trivial Moore space on which all continuous functions into Y are constant, Pacific J. Math. III (1984) 1-8.
  • Brandenburg, H. and Mysior, A., Short proof of an internal characterization of complete regularity, Canad. Math. Bull. 27 (1984) 461-462.
  • Burke, D. K., On subparacompact spaces, Proc. Amer. Math. Soc. 23 (1969) 655-663.
  • Burke, D. K., On p-spaces and wΔ-spaces, Pacific J. Math. 35 (1970) 285-296.
  • Burke, D. K., Subparacompact spaces, in: Proc. of the Washington State Univ. Topol. Conf. 1970, 39-49.
  • Burke, D. K., A note on Bing's example G, in: (Proc. Topol. Conf. VPI, 1973), Lecture Notes in Math., Springer, Berlin, (1974) 47-55.
  • Burke, D. K., Covering properties, in: Handbook of Set-Theoretic Topology, ed. by K. Kunen and J. E. Vaughan, North-Holland, Amsterdam (1984) 347-422.
  • Burke, D. K., PMEA and first countable, countably paracompact spaces, Proc. Amer. Math. Soc. 92 (1984) 455-460.
  • Carlson, J. W., B-completeness in nearness spaces, General Topol. and its Appl. 5 (1975) 263-268.
  • Carlson, J. W., Developable spaces and nearness structures, Proc. Amer. Math. Soc. 78 (1980) 573-579.
  • Ceder, J., Some generalizations of metric spaces. Pacific J. Math. 11 (1961) 105-125.
  • Chaber, J., On subparacompactness and related properties, General Topol. and its Appl. 10 (1979) 13-17.
  • Chaber, J., Perfect preimages of Moore spaces, Bull. Polish Acad. Sci. Math. 31 (1983) 31-34.
  • Chaber, J., A universal metacompact developable $T_1$-space of weight m, Fund. Math. 121 (1983) 81-88.
  • Chaber, J., On d-paracompactness and related properties. Fund. Math. 122 (1984) 175-186.
  • Chaber, J., Another universal metacompact developable $T_1$-space of weight m, Fund. Math. 122 (1984) 247-253.
  • Chaber, J. and Zenor, P., On perfect subparacompactness and a metrization theorem for Moore spaces, Topology Proc. 2 (1977) 401-407.
  • Charlesworth, A., A note on Urysohn's metrization theorem, Amer. Math. Monthly 83 (1976) 718-720.
  • Cohn, D. L., Measure Theory, Birkhäuser Verlag, Boston-Basel (1980).
  • Corson, H. H., Normality in subsets of product spaces, Amer. J, Math. 81 (1959) 785-796.
  • Creede, G., Concerning semi-stratifiable spaces, Pacific J. Math. 32 (1970) 47-54.
  • Dalgas, K.-P, Über Maßerweiterungen und maßkompakte Räume, Dissertation, Universität Köln (1978).
  • Dalgas, K.-P, A general extension theorem for group-valued measures, Math. Nachr. 106 (1982) 153-170.
  • Dieudonné, J., Sur les espaces uniformes complets, Ann. Sci. École Norm. Sup. 56 (1939) 277-291.
  • Dowker, C. H., An extension of Alexandroff's mapping theorem, Bull. Amer. Math. Soc. 54 (1948) 386-391.
  • Douwen van, E. K., The Pixley-Roy topology on spaces of subsets, in: Set-Theoretic Topology, ed. by G. M. Reed, Academic Press, New York (1977) 111-134.
  • Douwen van, E. K., There is no universal separable Moore space, Proc. Amer. Math. Soc. 76 (1979) 351-352.
  • Dranišnikov, A. N., Simultaneous annihilation of families of closed sets, ϰ-metrizable and stratifiable spaces, Soviet Math. 19 (1978) 1466-1469.
  • Dykes, N., Generalizations of realcompact spaces, Pacific J. Math. 33 (1970) 571-581.
  • Engelking, R., On functions defined on cartesian products, Fund. Math. 59 (1966) 221-231.
  • Engelking, R., General Topology, Polish Scientific Publ., Warszawa (1977).
  • Fleissner, W. G., If all normal Moore spaces are metrizable, then there is an inner model with a measurable cardinal, Trans. Amer. Math. Soc. 273 (1983) 365-373.
  • Fleissner, W. G., The normal Moore space conjecture and large cardinals, in: Handbook of Set-Theoretic Topology, ed. by K. Kunen and J. E. Vaughan, North-Holland, Amsterdam (1984) 733-760.
  • Fletcher, P. and Lindgren, W. F., Quasi-Uniform Spaces, Marcel Dekker, New York-Basel (1982).
  • Franklin, S. P. and Walker, R. C., Normality of powers implies compactness, Proc. Amer. Math. Soc. 36 (1972) 295-296.
  • Gardner, R. J., The regularity of Borel measures and Borel measure-compactness, Proc. London Math. Soc. 30 (1975) 95-113.
  • Gillman, L. and Jerison, M., Kings of continuous functions, Van Nostrand Reinhold Comp., New York (1960).
  • Gruenhage, G., Generalized metric spaces, in: Handbook of Set-Theoretic Topology, ed. by K. Kunen and J. E. Vaughan, North-Holland, Amsterdam (1984) 423-501.
  • Guthrie, J. A. and Henry, M., Metrization, paracompactness, and real-valued functions. Fund. Math. 95 (1977) 49-53.
  • Heath, R. W., On a question of H. Brandenburg, Abstract of a paper presented at the 1984 Topol. Conf, held at Auburn Univ., Auburn, Alabama.
  • Heath, R. W. and Michael, E., A property of the Sorgenfrey line, Compositio Math. 23 (1971) 185-188.
  • Heldermann, N. C., The category of D-completely regular spaces is simple. Trans. Amer. Math. Soc. 262 (1980) 437-446.
  • Heldermann, N. C., Developability and some new regularity axioms, Canad. J. Math. 33 (1981) 641-663.
  • Herrlich, H., Wann sind alle Abbildungen in Y konstant?, Math. Z. 90 (1965) 152-154.
  • Herrlich, H., ℰ-kompakte Räume, Math. Z. 96 (1967) 228-255.
  • Herrlich, H., Topologische Reflexionen und Coreflexionen, Lecture Notes in Math., Springer, Berlin (1968).
  • Herrlich, H., Categorical Topology, General Topol. and its Appl. 1 (1971) 1-15.
  • Herrlich, H., A concept of nearness. General Topol. and its Appl. 5 (1974) 191-212.
  • Herrlich, H., Categorical Topology 1971-1981, in: General Topol. and its Rel. to Mod. Anal, and Algebra V (Proc. Fifth Prague Topol. Symp., 1981) ed. by J. Novák, Heldermann Verlag, Berlin (1983) 279-383.
  • Herrlich, H. and Strecker, G., Algebra ∩ Topology = Compactness, General Topol, and its Appl. 1 (1971) 283-287.
  • Herrlich, H. and Strecker, G., Category Theory (sec. ed.). Heldermann Verlag, Berlin (1979).
  • Hewitt, E., Rings of real-valued continuous functions, I, Trans. Amer. Math. Soc. 64 (1948) 45-99.
  • Hödel, R. E., A note on subparacompact spaces, Proc. Amer. Math. Soc. 25 (1970) 842-845.
  • Howes, N. R., A note on transfinite sequences. Fund. Math. 106 (1980) 213-226.
  • Hušek, M., Continuous mappings on subspaces of products, in: Symp. Math. Vol. XVII (Convegno sugli Anelli di Funzioni Continue, INDAM, Rome, 1973), Academic Press, London (1976) 25-41.
  • Isbell, J. R., A note on complete closure algebras, Math. Systems Theory 3 (1969) 310-312.
  • Jones, F. B., Concerning normal and completely normal spaces, Bull. Amer. Math. Soc. 43 (1937) 671-679.
  • Jones, F. B., Moore spaces and uniform spaces, Proc. Amer. Math. Soc. 9 (1958) 483-486.
  • Jones, F. B., Constructing non-completely regular spaces, in: Topology Appl. (Proc. of the Topology Conf. Budva, 1972), ed. by D. Kurepa, Beograd (1973) 132-135.
  • Junnila, H., Neighbornets, Pacific J. Math. 76 (1978) 83-108.
  • Junnila, H., Three covering properties, in: Surveys in General Topol., ed. by G. M. Reed, Academic Press, New York (1980) 195-245.
  • Keesling, J., On the equivalence of normality and compactness in hyperspaces, Pacific J. Math. 33 (1970) 657-667.
  • Keesling, J., Normality and infinite product spaces. Adv. in Math. 9 (1972) 90-92.
  • Kerstan, J., Eine Charakterisierung der vollständig regulären Räume, Math. Nachr. 17 (1958) 27-46.
  • Kowalsky, H. J., Einbettung metrischer Räume, Arch. Math. 8 (1957) 336-339.
  • Kramer, T. R., A note on countably subparacompact spaces, Pacific J. Math. 46 (1973) 209-213.
  • Kunen, K., Set Theory. An Introduction to Independence Proofs, North-Holland, Amsterdam (1980).
  • Kuratowski, K., Topology, Vol. I, Academic Press, New York (1966).
  • Lutzer, D. J., Another property of the Sorgenfrey line, Compositio Math. 24 (1972) 359-363.
  • Mack, J. E., Math. Reviews 47 (1974) # 1034.
  • Marny, T., On epireflective subcategories of topological categories, General Topol. and its Appl. 10 (1979) 175-181.
  • Maxwell, C. N., An order relation among topological spaces, Trans. Amer. Math. Soc. 99 (1961) 201-204.
  • Mizokami, T., On closed images of perfect preimages of orthocompact developable spaces. Tsukuba J.. Math. 11 (1987) 219-225.
  • Moore, R. L., On the foundations of plane analysis situs, Trans. Armer. Math. Soc. 17 (1916) 131-164.
  • Moore, R. L., Foundations of Point Set Theory, Amer. Math. Soc. Colloq. Publ. 13, Providence (1962).
  • Morita, K., On the simple extension of a space with respect to a uniformity, I-IV, Proc. Jap. Acad. Ser. A. Math. Sci. 27 (1951) 65-72, 130-137, 166-171, 632-636.
  • Mrówka, S., Some properties of Q-spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. 5 (1957) 947-950.
  • Mrówka, S. , Further results on E-compact spaces, I, Acta Math. 120 (1968) 161-185.
  • Mysior, A., Two remarks on D-regular spaces, Glas. Mat. Ser. III 15 (35) (1980) 153-156.
  • Mysior, A., There is no universal space for developable second countable Hausdorff spaces, (unpublished manuscript).
  • Nagata, J.-I., A contribution to the theory of metrization, J. Inst. Polytech. Osaka City Univ. Ser. A. Math. 8 (1957) 185-192.
  • Noble, N., Products with closed projections, II, Trans. Amer. Math. Soc. 160 (1971) 169-183.
  • Nyikos, P. J., A provisional solution to the normal Moore space problem, Proc. Amer. Math. Soc. 78 (1978) 429-435.
  • Okuyama, A., Some generalizations of metric spaces, their metrization theorems and product spaces, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A., 9 (1967) 236-254.
  • Pareek, C. M., Moore spaces, semi-metric spaces and continuous mappings connected with them, Canad. J. Math. 24 (1972) 1033-1042.
  • Pasynkov, B. A., On the spectral decomposition of topological spaces, Amer. Math. Soc. Transl., 73 (1968) 87-134.
  • Pol, R. and Puzio-Pol, E., Remarks on cartesian products, Fund. Math. 93 (1976) 57-69.
  • Polkowski, L., On N. Noble's theorem concerning powers of spaces and mappings, Colloq. Math. 41 (1979) 215-217.
  • Preuss, G., Trennung und Zusammenhang, Monatsh. Math. 74 (1970) 70-87.
  • Ramer, A., Some problems of universal spaces, Bull. Acad. Pol. Sci. Sér. Sci. Math. 13 (1965) 291-294.
  • Reed, G. M. and Zenor, P., Metrization of Moore spaces and generalized manifolds, Fund. Math. 91 (1976) 203-210.
  • Romaguera, S., A characterization of strongly quasi-metrizable spaces, Math. Japon. 33 (1988) 583-585.
  • Reynolds, G., Alexandroff algebras and complete regularity. Proc. Amer. Math. Soc. 76 (1979) 322-326.
  • Rudin, M. E., Concerning abstract spaces, Duke Math. J. 17 (1950) 317-327.
  • Rudin, M. E., A normal space X for which X×1 is not normal, Fund. Math. 73 (1971) 179-186.
  • Rudin, M. E., The metrizability of Moore spaces, in: Studies in Topology, ed. by N. M. Stavrakas and K. R. Allen, Academic Press, New York (1975).
  • Rudin, M. E., The shrinking property, Canad. Math. Bull. 26 (1983) 385-388.
  • Shchepin, E. V., Real functions and canonical sets in Tychonoff products and topological groups, Russian Math. Surveys 31 (1976).
  • Šedivá-Trnková, V., The closure of classes of spaces under co-mappings, Czechoslovak. Math. J. 14 (89) (1964) 327-340 (in Russian).
  • Shirota, T., A class of topological spaces, Osaka J. Math. 4 (1952) 23-40.
  • Sierpiński, W., Cardinal and Ordinal Numbers, Polish Scientific Publ., Warszawa (1965).
  • Simon, P., A note on Rudin's example of a Dowker space, Comment. Math. Univ. Carolin. 12 (1971) 825-833.
  • Smith, J. C., Some properties of weak θ̅-refinable spaces, Proc. Amer. Math. Soc. 53 (1975) 511-517.
  • Solovay, R. M., Real-valued measurable cardinals, Proc. Sympos. Pure Math. 13 (1971) 397-428.
  • Sorgenfrey, R. H., On the topological product of paracompact spaces, Bull. Amer. Math. Soc. 53 (1947) 631-632.
  • Steiner, E., Wallman spaces and compactifications, Fund. Math. 61 (1968) 295-304.
  • Stone, A. H., Paracompactness and product spaces, Bull. Amer. Math. Soc. 54 (1948) 977-982.
  • Sun, S.-H. and Wang Y.-M., On two questions of D-completely regular spaces, Questions Answers Gen. Topology 6 (1988) 73-80.
  • Tall, F. D., Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture, Dissertationes Math. 148 (1977) 1-52.
  • Tanaka, H., Paracompactness of Pixley-Roy hyperspaces, I, Proc. Amer. Math. Soc. 85 (1982) 108-112.
  • Tukey, J. W., Convergence and Uniformity in Topology, Ann: of Math. Studies 2, Princeton (1940).
  • Tikhonov, A., Über die topologische Erweiterung von Räumen, Math. Ann. 102 (1930) 544-561.
  • Uspenskii, V. V., A characterization of realcompactness in terms of the topology of pointwise convergence on the function space, Comment. Math. Univ. Carolin. 24 (1983) 121-126.
  • Velichko, N. V., On the space of closed subsets, Siberian. Math. J. 16 (1975) 484-486.
  • Weil, A., Sur les espaces à structure uniforme et sur la topologie générale, Paris 1938.
  • Wicke, H. H. and Worrell, Jr., J. M., Characterizations of developable spaces, Canad. J. Math. 17 (1965) 820-830.
  • Worrell Jr., J. M., Upper semi-continuous decompositions of developable spaces, Proc. Amer. Math. Soc. 16 (1965) 485-490.
  • Younglove, J. N., A locally connected, complete Moore space on which every real-valued continuous function is constant, Proc. Amer. Math. Soc. 20 (1969) 527-530.
  • Zenor, P., A note on Z-mappings and WZ-mappings, Proc. Amer. Math. Soc. 23 (1969) 273-275.
  • Zenor, P., Some continuous separation axioms, Fund. Math. 90 (1976) 143-158.
Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-65e6ea69-1542-41ee-aa40-cf72143c5063
Identyfikatory
ISBN
83-01-09071-5
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

rozwiń roczniki

JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.