Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl
Zapraszamy na https://bibliotekanauki.pl
Zawartość
Pełne teksty:
Warianty tytułu
Abstrakty
CONTENTS
0. Conventions................................................................................................................................... 5
1. Introduction............................................................................................................................................. 5
CHAPTER I. TOOLS AND THE CONSTRUCTION OF SPECIAL POINTS............................... 10
2. Tools........................................................................................................................................................ 10
3. Extension of open sets......................................................................................................................... 10
4. Construction of special points in X*................................................................................................... 12
CHAPTER II. EFFECTIVE PROOFS USING REMOTE POINTS................................................. 16
5. Remote points and extremal disconnectedness at points........................................................... 16
6. Remote points and nonhomogeneity................................................................................................ 17
7.Čech-Stone compactifications and products.................................................................................... 19
8. When "extremally disconnected at" implies remote....................................................................... 22
9. Far points, remote points, and nonhomogeneity............................................................................ 24
CHAPTER III. OTHER APPLICATIONS OF REMOTE POINTS................................................... 25
10. Two examples on extremal disconnectedness............................................................................ 25
11. A partition of R*.................................................................................................................................... 26
12. Extremal disconnectedness and C*-embedding......................................................................... 27
13. Connected compactifications........................................................................................................... 28
CHAPTER IV. PROPERTIES OF REMOTE POINTS.................................................................... 30
14: The structure of remote points.......................................................................................................... 30
15. Nonhomogeneity of spaces of special points............................................................................... 31
16. Special points and Baire spaces..................................................................................................... 32
17. Pseudocompact spaces between X and βX.................................................................................. 32
CHAPTER V. MISCELLANEOUS REMARKS................................................................................ 36
18. Zero-dimensional spaces................................................................................................................. 36
19. Q, Q*, Q**, Q***,................................................................................................................................... 37
20. Retractions from βX onto X*.............................................................................................................. 38
21. Products of remainders..................................................................................................................... 39
22. Questions............................................................................................................................................. 40
REFERENCES................................................................................................................................... 42
INDEX................................................................................................................................................... 44
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
188
Liczba stron
45
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CLXXXVIII
Daty
wydano
1981
Twórcy
autor
Bibliografia
- [1] B. Banaschewski, Über nulldimensionale Räume, Math. Nachr. 13 (1955), 129-140 [18.1].
- [2] A. R. Bernstein, A new kind of compactness for topological spaces, Fund. Math. 66 (1971), 185-193 [17.3, 17.14].
- [3] R. H. Bing, A countable connected Hausdorff space, Proc. Amer. Math. Soc. 4 (1953), 474 [13.5].
- [4] R. L. Blair and E. K. van Douwen, unpublished notes [27].
- [5] W. Comfort, Retractions and other continuous maps from ßX onto βX — X, Trans. Amer. Math. Soc. 114 (1965), 1-9 [20.2].
- [6] E. K. van Douwen, Martin's axiom and pathological points, 1974 m.s. [1.18].
- [7] E. K. van Douwen, Why certain Čech-Stone remainders are not homogeneous, Coll. Math. [6.10, 9.1, 9.3].
- [8] E. K. van Douwen, Nonhomogeneity of products of preimages and π-weight, Proc. Amer. Math. Soc. 69 (1978), 183-192.
- [9] E. K. van Douwen, When Пβ and Пβ are homeomorphic, Bull. Acad. Pol. Sci. 26 (1978), 271-274 [1.13, 7.1, 7.14].
- [10] E. K. van Douwen βX, Retractions from βX onto βX-X, Gen. Top. Appl., 9 (1978), 169-173 [20.2].
- [11] E. K. van Douwen, Some countable examples, in preparation [1.17, 14.3].
- [12] E. K. van Douwen, Homogeneity of βG if G is a topological group, Coll. Math. 41 (1979), 193-199 [15.3].
- [13] E. K. van Douwen, Subcontinua and nonhomogeneity of $βℛ^+ - ℛ^+$, in preparation [6.10].
- [14] E. K. van Douwen, and D. J. Lutzer, On the classification of stationary sets, Michigan Math. J. 26 (1979), 47-64 [1.2].
- [15] R. Engelking, General topology, Polish Scientific Publishers, Warszawa 1977.
- [16] A. Emeryk and W. Kulpa, The Sorgenfrey line has no connected compactification, Comm. Math. Univ. Car. 18 (1977), 483-487 [22.12].
- [17] N. J. Fine and L. Gillman, Extension of continuous functions in βN, Bull. Amer. Math. Soc. 66 (1960), 376-381 [6.8, 20.3].
- [18] N. J. Fine and L. Gillman, Remote points in βR, Proc. Amer. Math. Soc. 13 (1962), 29-36 [1.16, 1.18, 4.11, 17.15].
- [19] Z. Frolik, Sums of ultrafilters. Bull. Amer. Math. Soc. 73 (1967), 87-91 [6.10].
- [20] Z. Frolik, Non-homogeneity of βP-P, Comment. Math. Univ. Car. 8 (1967), 705-709 [1.1, 6.8, 6.10, 9.3].
- [21] C. Gates, A study of remote points of metric spaces, University of Kansas, Ph, D. thesis [1.18, 16.4].
- [22] L. Gillman and M. Jerison, Stone—Čech compactification of a product, Arch. Math. 10 (1959), 443-446 [1.11, 7.1, 7.14].
- [23] L. Gillman and M. Jerison, Rings of continuous functions, Van Nostrand, Princeton, 1960.
- [24] J. Ginsberg and V. Saks, Some applications of ultrafilters in topology, Pacific J. Math. 57 (1975), 403-418 [17.2, 17.3, 17.4, 17.5, 17.14].
- [25] A. M. Gleason, Projective topological spaces, Ill. J. Math. 2 (1958), 482-489 [10.2, 12.2].
- [26] I. Glicksberg, Stone-Čech compactification of products, Trans. Amer. Math. Soc. 90 (1959), 369-382 [1.11, 6.9, 7.1, 7.4, 7.13, 17.5, 21.1].
- [27] M. Mandelker, Prime z-ideal structure of C(R), Fund. Math. 63 (1968), 145-166 [1.18].
- [28] M. Mandelker, Round z- filters and round subsets of βX, Israel J. Math. 7 (1969), 1-8 [1.18, 14.4].
- [29] J. Novák, On the cartesian product of two compact spaces. Fund. Math. 40 (1953), 106-112 [17.2].
- [30] G. Orwell, Animal farm, [1.3].
- [31] I. I. Parovičenko, On a universal bicompact of weight ℵ, Dokl. Akad. Nauk SSSR 150 (1963), 36-39 ≡ Sov. Math. Dokl. 4 (1963), 592-595 [22.12].
- [32] D. Plank, On a class of subalgebras of C(X) with applications to βX -X, Fund. Math. 64 (1969), 41-54 [1.18, 22.12].
- [33] J. R. Porter and R. C. Woods, Nowhere dense subsets of metric spaces with applications to S tone-Čech compactifications, Canad. J. Math. 4 (1972), 622-630 [1.18, 8.5].
- [34] M. E. Rudin, personal communication, [4.11].
- [35] W. Rudin, Homogeneity problems in the theory of Čech compactifications, Duke Math. J. 23 (1956), 409-419, 633 [6.10, 15.1, 22.12].
- [36] S. Saks and R. M. Stephenson, Jr., Products of m-compact spaces. Proc. Amer. Math. Soc. 28 (1971), 279-288 [17.14].
- [37] N. S. Šanin, On special extensions of topological spaces, C. R, (Doklady) Acad. Sci. URSS 38 (1943), 6-9 (Cited in [15], p. 480).
- [38] Yu. M. Smirnov, Zusammenhang und bogenweiser Zusammenhang von Kompaktifizierungen und deren Adjunkten, in: Contributions to extension theory of topological spaces, eds. J. Flacksmeyer, H. Poppe and F. Terpe, Berlin 1969, p. 211-216 [13.4].
- [39] Yu. M. Smirnov, Mat. Sbornik 71 (1966), 454-482 (Cited in [38]).
- [40] M. Starbird, personal communication, [13.5].
- [41] A. Szymański, On the existence of ω-points, Proc. Amer. Math. Soc. [6.8, 20.3].
- [42] A. D. Taimanov, On extension of continuous mappings of topological spaces, Mat. Sbornik 31 (1952), 459-463 (Russian, cited in [15]) [21.1].
- [43] R. Telgársky, Scattered compactifications and points of extremal disconnectedness, Bull. Acad. Polon. Sci. Ser. Math. Astronom. Phys. 25 (1977), 155-159.
- [44] H. Terasaka, On the cartesian product of compact spaces, Osaka J. Math. (1952), 11-15 [17.2].
- [45] J. Wisliceni and J. Flachsmeyer, The power and the structure of the lattice of all compact extensions of a completely regular space, Dokl. Akad. Nauk SSSR 165 (1965), 258-260 = Sov. Math. Dokl. 6 (1965), 1423-1425.
- [46] R. G. Woods, Co-absolutes of Stone-Čech compactifications, Pacific J. Math. 37 (1971), 545-560 [12.5].
- [47] R. G. Woods, Some $ℵ_0$-bounded subsets of Stone-Čech compactifications, Israel J. Math. 9 (1971), 250-256 [1.18, 11.3].
- [48] R. G. Woods, personal communication [22.12].
- [49] S. B. Chae and J. H. Smith, Remote points and G-spaces, Top. Appl. 11 (1980), 243-246.
- [50] E. K. van Douwen, Spaces without remote points. Pacific J. Math, (to appear).
- [51] E. G. Sklyarenko, Some questions in the theory of bicompactifications, Izv. Akad. Nauk SSSR, Ser. Mat. 26 (1962), 427-452. ≡ Amer. Math. Soc. Transl. Ser. (2) 58 (1966), 216-244.
- [52] T. Terada, On remote points in βX-X, Proc. Amer. Math. Soc. 77 (1979), 264-266.
Języki publikacji
| EN |
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-334f9e04-e784-4a82-8eb3-b9605ad33a80
Identyfikatory
ISBN
83-01-01251-X
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.