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Warianty tytułu
Abstrakty
CONTENTS
Introduction.......................................................................................................................................................... 5
I. PRELIMINARIES.............................................................................................................................................. 7
§ 1. The closures of open subsets in r. o.-equivalent topologies............................................................. 7
§ 2. The r. o.-maximal topologies.................................................................................................................... 9
§ 3. The H-closed maximal spaces................................................................................................................ 10
§ 4. R. o.-equivalence of extensions............................................................................................................... 10
§ 5. 0-continuous maps.................................................................................................................................... 11
§ 6. The Henriksen-Jerison and skeletal maps........................................................................................... 13
II. H-CLOSED EXTENSIONS OF HAUSDORFF SPACES.................................................................................... 14
§ 1. The set of 77-closed extensions of given Hausdorff space............................................................... 14
5 2. Proper maps................................................................................................................................................ 16
§ 3. Decompositions of proper maps............................................................................................................ 18
§ 4. An application to IT-closed extensions................................................................................................... 19
§ 5. The case of compact-like spaces........................................................................................................... 22
§ 6. The case of minimal Hausdorff spaces................................................................................................. 25
III. EXTREMALLY DISCONNECTED RESOLUTIONS OF HAUSDORFF SPACES................................. 26
§ 1. The set of irreducible maps onto a given Hausdorff space X............................................................ 26
§ 2. R. o.-minimal irreducible maps............................................................................................................... 30
§ 3. Extremally disconnected resolutions...................................................................................................... 31
IV. COMMUTATION OF H-CLOSED EXTENSIONS AND E. D. RESOLUTIONS...................................... 35
§ 1. Commutativity in a pullback diagram...................................................................................................... 35
§ 2. Commutativity in a pushout diagram ..................................................................................................... 37
V. PROJECTIVE AND INJECTIVE HAUSDORFF SPACES......................................................................... 39
§ 1. H-closed projective spaces. A definition and motivations.................................................................. 41
§ 2. The case of compact-like spaces........................................................................................................... 42
§ 3. Projectiveness for arbitrary H-closed spaces....................................................................................... 44
§ 4. Projectiveness for arbitrary Hausdorff spaces...................................................................................... 45
§ 5. Injective extremally disconnected spaces............................................................................................. 46
§ 6. Injective Hausdorff spaces....................................................................................................................... 48
Bibliography......................................................................................................................................................... 51
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne
tom/nr w serii:
66
Liczba stron
52
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom LXVI
Daty
wydano
1969
Twórcy
autor
- Silesian University, Katowice
- Wrocław University
autor
- Silesian University, Katowice
- Wrocław University
Bibliografia
- [1] P. S. Alexandroff et P. S. Urysohn, Mémoire sur les espaces topologiques compacts, Verh. K. Akademie Amsterdam, Deel XIV, Nr 1 (1929), pp. 1-96.
- [2] B. Banaschewski, The Katětov and Čech-Stone expansions, Canadian M. J. 11 (1959), pp. 1-4.
- [3] B. Banaschewski, Über Hausdorffsch-minimale Erweiterungen von Räumen, Archiv der Math. 12 (1961), pp. 355-365.
- [4] J. Flachsmeyer, Topologische Projektivräume, Math. Nachrichten 26 (1963), pp. 57-66.
- [5] J. Flachsmeyer, Zur Theorie der H-abgeschlossenen Erweiterungen, Math. Zeitschrift 94 (1966), pp. 349-381.
- [6] С. В. Фомин, К теории расширений топологических пространств, Матем. Сборник 50 (1940), pp. 285-294.
- [7] С. В. Фомин и С. Илиадис, Метод центрированных систем в теории топологических пространств, Успехи Математических Наук 21 (1966), pp. 47-76.
- [8] P. Freyd, Abelian categories, New York, Evanston and London 1964.
- [9] A. M. Gleason, Projective topological spaces, Illinois Journal of Math. 2 (1958), pp. 482-489.
- [10] M. Henriksen and J. R. Isbell, Some properties of compactifications, Duke M. J. 25 (1958), pp. 83-106.
- [11] M. Henriksen and M. Jerison, Minimal projective extensions of compact spaces, Duke M. J. 32 (1965), pp. 291-295.
- [12] H. Herrlich and G-. E. Strecker, H-closed spaces and reflective subcategories, a mimeographed note, 1967.
- [13] E. Hewitt, A problem of set-theoretic topology, Duke M. J. 10 (1943), pp. 309-333.
- [14] С. Илиадис, Абсолюты хаусдорфовых пространств, ДАН СССР 149 (1963), pp. 22-25.
- [15] С. Илиадис, Характеризация пространств при помощи Н-замкнутых расширений, ДАН СССР 149 (1963), pp. 1015-1018.
- [16] M. Katětov, Über H-abgeschlossene und bikompakte Räume, Časopis matem. fys. 69 (1940), pp. 36-49.
- [17] M. Katětov, On H-closed extensions of topological spaces, Časopis matem. fys. 72 (1947), pp. 17-32.
- [18] M. Katětov, О пространствах не содержащих непересекающихся плотных множеств, Матем. Сборник 21 (1947), pp. 3-12.
- [19] J. Mioduszewski and L. Rudolf, On projective spaces and resolutions in categories of completely regular spaces, Colloq. Math. 18 (1967), pp. 185-196.
- [20] B. Mitchell, Theory of categories, New York-London 1964.
- [21] В. И. Пономарев, Об абсолюте топологического пространства, ДАН СССР 149 (1963), pp. 26-29.
- [22] J. Rainwater, A note on projective resolutions, Proc. Amer. Math. Soc. 10 (1959), pp. 734-735.
- [23] A. Ramanathan, Maximal Hausdorff spaces, Proc. Indian. Acad. Sci. Sect. A, 26 (1947), pp. 31-42.
- [24] M. H. Stone, Algebraic characterisations of special Boolean rings, Fund. Math. 29 (1937), pp. 223-303.
- [25] Dona P. Strauss, Extremally disconnected spaces, Proc. Amer. Math. Soc. 18 (1967), pp. 305-310.
- [26] Н. В. Величко, Н-замкнутые топологические просранства, Матем. Сборник 70 (I960), pp. 98-112.
- [27] Н. В. Величко, О продолжении отображений топологических простронств, ДАН СССР 177 (1967), pp. 1255-1258.
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