H-closed and extremally disconnected Hausdorff spaces

J. Mioduszewski ; L. Rudolf

GDML_Books, (1969), p.

Résumé

CONTENTSIntroduction.......................................................................................................................................................... 5I. 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........................................................................................... 13II. H-CLOSED EXTENSIONS OF HAUSDORFF SPACES.................................................................................... 14§ 1. The set of 77-closed extensions of given Hausdorff space............................................................... 145 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................................................................................................. 25III. 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...................................................................................................... 31IV. COMMUTATION OF H-CLOSED EXTENSIONS AND E. D. RESOLUTIONS...................................... 35§ 1. Commutativity in a pullback diagram...................................................................................................... 35§ 2. Commutativity in a pushout diagram ..................................................................................................... 37V. 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....................................................................................................................... 48Bibliography......................................................................................................................................................... 51

Détail

Zbl 0204.22404

EUDML-ID : urn:eudml:doc:268441