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Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
Chapter 0
0. Introduction...................................................................................................... 5
1. Outline of thesis.............................................................................................. 7
2. Notation............................................................................................................ 8
Chapter I
0. Definitions........................................................................................................ 9
1. Relations among the covering axioms...................................................... 10
2. Covering axioms and collection wise normality....................................... 13
3. Covering axioms and countability conditions........................................... 18
Chapter II
0. Preliminaries.................................................................................................. 21
1. The consistency proof................................................................................... 24
2. Topological consequences......................................................................... 31
3. Bing's example............................................................................................... 37
4. To be continued............................................................................................. 39
Chapter III
0. Prehistory......................................................................................................... 42
1. History............................................................................................................... 43
2. Everything is equivalent................................................................................. 47
Bibliography.............................................................................................................. 51
Chapter 0
0. Introduction...................................................................................................... 5
1. Outline of thesis.............................................................................................. 7
2. Notation............................................................................................................ 8
Chapter I
0. Definitions........................................................................................................ 9
1. Relations among the covering axioms...................................................... 10
2. Covering axioms and collection wise normality....................................... 13
3. Covering axioms and countability conditions........................................... 18
Chapter II
0. Preliminaries.................................................................................................. 21
1. The consistency proof................................................................................... 24
2. Topological consequences......................................................................... 31
3. Bing's example............................................................................................... 37
4. To be continued............................................................................................. 39
Chapter III
0. Prehistory......................................................................................................... 42
1. History............................................................................................................... 43
2. Everything is equivalent................................................................................. 47
Bibliography.............................................................................................................. 51
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
148
Liczba stron
53
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CXLVIII
Daty
wydano
1977
Twórcy
autor
Bibliografia
- Bibliography
- [1] K. Alster and T. Przymusiński, Normality and Martin's axiom, Fund. Math. 91(1976), pp. 123-131.
- [2] G. Aquaro, Point countable open coverings in countably compact spaces, pp. 39-41 in General Topology and its Relations to Modern Analysis and Algebra II, Proceedings of the Second Prague Topological Symposium, 1966, Academic Press, New York 1967.
- [3] A. V. Arhangel'skiǐ, On the cardinality of bicompacta satisfying the first axiom of countability, Soviet Math. Dokl. 10 (1969), pp. 951-955.
- [4] C. E. Aull, Paracompact subsets, pp. 45-51 in General Topology and its Relations to Modern Analysis and Algebra II, Proceedings of the Second Prague Topological Symposium, 1966, Academic Press, New York 1967.
- [5] R. H. Bing, Metrization of topological spaces, Canad. J. Math. 3 (1951), pp. 175-186.
- [6] R. H. Bing, A translation of the normal Moore space conjecture, Proc. Amer. Math. Soc. 16 (1965), pp. 612-619.
- [7] L. Bukovsky, Borel subsets of metric separable spaces, pp. 83-86 in General Topology and its Relations to Modern Analysis and Algebra. II, Proceedings of the Second Prague Topological Symposium, 1966, Academic Press, New YoTk 1967.
- [8] A. Charlesworth, R. Hodel and F. Tall, On a theorem of Jones and Heath concerning discrete subspaces, Colloq. Math. 34 (1975), pp. 33-37.
- [9] P. J. Cohen, Set Theory and the Continuum Hypothesis, W. A. Benjamin, New York 1966,
- [10] J. Dieudonné, Une généralisation des espaces compacts, J. Math. Pures Appl. 23 (1944), pp. 65-76.
- [11] C. H. Dowker, On countably paracompact spaces, Canad. J. Math. 3 (1951), pp. 219-224.
- [12] C. H. Dowker, On a theorem of Hanner, Ark. for Mat. 2 (1952), pp. 307-313.
- [13] J. Dugundji, Topology, Allyn and Bacon, Boston 1966.
- [14] W. Easton, Powers of regular cardinals, Thesis, Princeton University, 1964.
- [15] R. Engelking, Outline of General Topology, North-Holland and Polish Scientific Publ., Amsterdam—Warszawa 1968.
- [16] B. Fitzpatrick and D. R. Traylor, Two theorems on metrizability of Moore spaces, Pacific J. Math. 19 (1966), pp. 259-264.
- [17] W. G. Fleissner, Normal Moore spaces in the constructible universe, Proc. Amer. Math. Soc. 46 (1974), pp. 294-298.
- [18] W. G. Fleissner, A normal collectionwise Hausdorff not collectionwise normal space, Gen. Top. Appl. 6 (1976), pp. 57-64.
- [19] K. Gödel, Consistency-proof for the generalized continuum hypothesis, Proc. Nat. Acad. Sci. U.S.A. 25 (1939), pp. 220-224.
- [20] J. de Groot, Discrete subspaces of Hausdorff spaces, Bull. Acad. Polon. Sci, Sér. Sci. Math. Astronom. Phys. 13 (1966), pp. 637-544.
- [21] F. Hausdorff, Problème 58, Fund. Math. 20 (1933), p. 286.
- [22] R. W. Heath, Screenability, pointwise paracompactness and metrization of Moore spaces, Canad. J. Math. 16 (1964), pp. 763—770.
- [23] J. Isbell, Memories on spaces of large cardinal number, Czechoslovak Math. J. 14 (1964), pp. 383-385.
- [24] T. J. Jech, Lectures in set theory with particular emphasis on the method of forcing, Lect. Notes Math. 217, Springer-Verlag, Berlin 1971.
- [25] R. B. Jensen, The fine structure of the constructible hierarchy, Ann. Math. Logic 4 (1972), pp. 229-308.
- [26] F. B. Jones, Concerning normal and completely normal spaces, Bull. Amer. Math. Soc. 43 (1937), pp. 671-677.
- [27] K. Kuratowski, Topology, vol. I, Academic Press, PWN—Polish Scientific Publishers, New York, London, Warszawa 1966.
- [28] D. A. Martin and R. M. Solovay, Internal Cohen extensions, Ann. Math. Logic 2 (1970), pp. 143-178.
- [29] M. J. Mansfield, On countably paracompact normal spaces, Canad. J. Math. 9 (1957), pp. 443-449.
- [30] L. F. McAuley, A note on complete collectionwise normality and paracompactness, Proc. Amer. Math. Soc. 9 (1958), pp. 796-799.
- [31] T. Menas, On strong compactness and supercompactness, Thesis, University of California, Berkeley 1973.
- [32] E. Michael, A note on paracompact spaces, Proc. Amer. Math. Soc. 4 (1953), pp. 831-838.,
- [33] E. Michael, Point-finite and locally finite coverings, Canad. J. Math. 7 (1955), pp. 275-279.
- [34] E. Michael, Another note on paracompact spaces, Proc. Amer. Math. Soc. 8 (1957), pp. 822-828.
- [35] J. D. Monk, Introduction to Set Theory, McGraw-Hill, New York 1969.
- [36] R. L. Moore, Foundations of Point Set Theory, Amer. Math. Soc. Coll. Publ. 13, 1932. Rev. ed., Providence 1962.
- [37] K. Morita, Star-finite coverings and the star-finite property, Math. Jap. 1 (1948), pp. 60-68.
- [38] K. Nagami, Paracompactness and strong screenability, Nagoya Math. J. 8 (1955), pp. 83-88.
- [39] F. Rothberger, On some problems of Hausdorff and of Sierpiński, Fund. Math. 35 (1948), pp. 29-46.
- [40] B. Šapirovskiĭ, On separability and metrizability of spaces with Souslin's condition, Soviet Math. Dokl. 13 (1972), pp. 1633-1638.
- [41] J. R. Shoenfield, Unramfied forcing, Proc. Sympos. Pure Math. 13, Part I (1971), pp. 357-382.
- [42] W. Sierpiński, Sur un problème de M. Hausdorff, Pand. Math. 30 (1938), pp. 1-7.
- [43] Yu. M. Smirnov, On strongly paracompact spaces (in Russian), Izv. Akad. Nauk SSSR ser. mat. 20 (1956), pp. 253-274.
- [44] R. M. Solovay and S. Tennenbaum, Interated Cohen extensions and Souslin's problem, Ann. of Math. 94 (1971), pp. 201-245.
- [45] F. D. Tall, Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems, Thesis, University of Wisconsin, Madison 1969.
- [46] F. D. Tall, A set-theoretic proposition implying the metrizability of normal Moore spaces, Proc. Amer. Math. Soc. 33 (1972), pp. 195-198.
- [47] F. D. Tall, On the existence of non-metrizable metacompact normal Moore spaces, Canad. J. Math. 20 (1974), pp. 1-6.
- [48] F. D. Tall, How separable is a space? That depends on your set theory! Proc. Amer. Math. Soc. 46 (1974), pp. 310-314.
- [49] F. D Tall, The countable chain condition versus separability — applications of Martin's Axiom, Gen. Top. Appl. 4 (1974), pp. 315-340.
- [50] D. R. Traylor, A note on metrization of Moore spaces, Proc. Amer. Math. Soc. 14 (1963), pp. 804-805.
- [51] D. R. Traylor, Normal, separable Moore spaces and normal Moore spaces, Duke Math. J. 30 (1963), pp. 485-494.
- [52] D. R. Traylor, Concerning metrisability of pointwise paracompact Moore spaces, Canad. J. Math. 16 (1964), pp. 407-411.
- [53] D. R. Traylor, Metrizability and completeness in normal Moore spaces, Pacific J. Math. 17 (1966), pp. 381-390.
- [54] D. R. Traylor, Metrizability in normal Moore spaces, ibid. 19 (1966), pp. 175-181.
- [55] D. R. Traylor, On normality, pointwise paracompactness and the metrization question, pp. 286-289 in Topology Conference Arizona State University 1967, Tempe, Arizona, 1968.
- [56] R. W. Heath, Separability and $ℵ_1$-compactness, Colloq,. Math. 12 (1964), pp. 11-14.
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