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H-closed and extremally disconnected Hausdorff spaces

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Mioduszewski J., Rudolf L.

Instytut Matematyczny Polskiej Akademii Nauk

EN

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

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On projective spaces and resolutions in categories of completely regular spaces

56%

Mioduszewski J., Rudolf L.

Colloquium Mathematicum

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1967

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tom 18

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nr 1

185-196

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θ-continuous extensions of maps on τX

38%

Rudolf L.

Fundamenta Mathematicae

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1972

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tom 74

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nr 2

111-131

4

Extending maps from dense subspaces .

38%

Rudolf L.

Fundamenta Mathematicae

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1972-1973

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tom 77

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nr 2

171-190

5

On compactification of T₀-spaces

33%

Rudolf L.

Colloquium Mathematicum

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1967

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tom 17

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nr 1

41-50

Ograniczanie wyników

2 Colloquium Mathematicum

2 Fundamenta Mathematicae

5 Rudolf L.

2 Mioduszewski J.

2 1972

1 1969

2 1967

H-closed and extremally disconnected Hausdorff spaces

On projective spaces and resolutions in categories of completely regular spaces

θ-continuous extensions of maps on τX

Extending maps from dense subspaces .

On compactification of T₀-spaces