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Baire spaces

100%

Haworth R. C., McCoy R. A.

Instytut Matematyczny Polskiej Akademii Nauk

EN

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

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The Freudenthal compactification

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Dickman R. F., McCoy R. A.

Instytut Matematyczny Polskiej Akademii Nauk

EN

CONTENTS 1. Introduction...................................................5 2. ℬ-filters and ℬ-compactifications..................6 3. The weight of φX.........................................12 4. Other properties of φX................................15 5. Extensions of maps and subspaces............21 6. Subordinate subsets of C*(X)......................25 7. Quasi-component spaces...........................30 8. References.................................................33

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Galois spaces, representable spaces and strongly locally homogeneous spaces

75%

Fletcher P., McCoy R. A.

Fundamenta Mathematicae

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1971-1972

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tom 73

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nr 1

85-91

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Function spaces with intervals as domain spaces

56%

McCoy R. A.

Fundamenta Mathematicae

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1975-1976

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tom 90

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nr 2

189-198

5

The open-cover topology on function spaces

47%

McCoy R. A.

Fundamenta Mathematicae

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1979

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tom 104

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nr 2

69-73

Ograniczanie wyników

3 Fundamenta Mathematicae

5 McCoy R. A.

1 Dickman R. F.

1 Fletcher P.

1 Haworth R. C.

1 1988

1 1979

1 1977

1 1976

1 1971

Baire spaces

The Freudenthal compactification

Galois spaces, representable spaces and strongly locally homogeneous spaces

Function spaces with intervals as domain spaces

The open-cover topology on function spaces