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Baire spaces

Seria
Rozprawy Matematyczne tom/nr w serii: 141 wydano: 1977
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Abstrakty
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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
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
  • Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA
autor
  • Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061, USA
Bibliografia
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