Baire spaces

Haworth, R. C.; McCoy, R. A

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Tytuł książki

Baire spaces

Autorzy

R. C. Haworth R. A McCoy

Seria

Rozprawy Matematyczne tom/nr w serii: 141 wydano: 1977

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CONTENTS

Introduction............................................................................................................ 5

I. Basic properties of Baire spaces................................................................... 6
1. Nowhere dense sets............................................................................................... 6
2. First and second category sets............................................................................. 8
3. Baire spaces............................................................................................................. 11
4. Isolated points and Baire spaces......................................................................... 15

II. Concepts related to Baire spaces................................................................ 18

1. Baire spaces in the strong sense................................................................ 18
2. Baire category theorem........................................................................................... 19
3. Complete type properties which imply Baire...................................................... 19
4. Minimal spaces........................................................................................................ 24

III. Characterizations of Baire spaces............................................................... 29
1. Blumberg type theorems........................................................................................ 29
2. Covering and filter characterizations.................................................................... 36
3. Characterizations of Baire spaces involving pseudo-complete spaces....... 37
4. The Banach-Mazur game........................................................................................ 38
5. Countably-Baire spaces......................................................................................... 41

IV. The dynamics of Baire spaces..................................................................... 44
1. Images and inverse images of Baire spaces.................................................... 44
2. Baire space extensions.......................................................................................... 49
3. Hyperspaces and functions spaces..................................................................... 53

V. Products of Baire spaces............................................................................... 56
1. Finite products.......................................................................................................... 56
2. Infinite products........................................................................................................ 60
3. k-Baire spaces.......................................................................................................... 64
4. Product counterexamples....................................................................................... 69

Bibliography........................................................................................................... 72

Słowa kluczowe

Tematy

Wydawca

Instytut Matematyczny Polskiej Akademii Nauk

Miejsce publikacji

Warszawa

Copyright

Seria

Rozprawy Matematyczne tom/nr w serii: 141

Liczba stron

73

Liczba rozdzia³ów

Opis fizyczny

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA

Daty

wydano

1977

Twórcy

autor

R. C. Haworth

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA

autor

R. A McCoy

Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA

Bibliografia

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[42] McCoy, R. A., A filter characterization of regular Baire spaces, Proc. Amer. Math. Soc. 40 (1973), pp. 268-270.
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[45] McCoy, R. A., Function spaces with intervals as domain space. Fund. Math. 90(1976), pp. 189-198
[46] McCoy, R. A Unions of first category spaces, (to appear).
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Baire spaces

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