Hausdorff Compactifications: A Retrospective

1998 ◽  
pp. 631-667
Author(s):  
Richard E. Chandler ◽  
Gary D. Faulkner
Keyword(s):  
Hausdorff Compactifications

Hausdorff Compactifications as Epireflections

1975 ◽  
Vol 17 (5) ◽  
pp. 675-677 ◽  
Author(s):  
W. N. Hunsaker ◽  
S. A. Naimpally
Keyword(s):  
Continuous Functions ◽  
One To One ◽  
Hausdorff Compactifications ◽  
The One

AbstractWe answer the following problem posed by Herrlich in the affirmative: “Can the Freudenthal compactification be regarded as a reflection in a sensible way?” This is accomplished by exploiting the one-to-one correspondence between proximities compatible with a given Tihonov space and compactifications of that space. We give topological characterizations of proximally continuous functions for the proximities associated with the Freudenthal and Fan-Gottesman compactifications.

Hausdorff compactifications in ZF

2019 ◽  
Vol 258 ◽  
pp. 79-99
Author(s):  
Kyriakos Keremedis ◽  
Eliza Wajch
Keyword(s):  
Hausdorff Compactifications

scholarly journals Multiple points and Wallman compactifications

1975 ◽  
Vol 20 (3) ◽  
pp. 274-280
Author(s):  
Olav Njastad
Keyword(s):  
Quotient Space ◽  
Affirmative Answer ◽  
Multiple Points ◽  
Hausdorff Compactifications ◽  
Tychonoff Spaces ◽  
Special Case

Banaschewski (1963) and Frink (1964) generalized the compactification procedure of Wallman to obtain Hausdorff compactifications of Tychonoff spaces. Numerous papers have been devoted to the problem whether all Hausdorff compactifications may be obtained in this way, and for many classes of compactifications an affirmative answer has been given. This note is a contribution in this direction. We show that if a (Hausdorff) compactification αX of X is the quotient space of a Wallman compactification γX in such a way that the set of multiple points of αX with respect to γX is not too large, then αX too is a Wallman compactification. The results are generalizations of earlier results of Steiner and Steiner (1968) and by the author (1966) for the special case that γX is the Stone Čech-compactification.

scholarly journals Magill-type theorems for mappings

2004 ◽  
Vol 2004 (26) ◽  
pp. 1379-1391 ◽  
Author(s):  
Giorgio Nordo ◽  
Boris A. Pasynkov
Keyword(s):  
Hausdorff Compactifications ◽  
Tychonoff Spaces

Magill's and Rayburn's theorems on the homeomorphism of Stone-Čech remainders and some of their generalizations to the remainders of arbitrary Hausdorff compactifications of Tychonoff spaces are extended to some class of mappings.

A CONSTRUCTION FOR TOPOLOGICAL EXTENSIONS

2011 ◽  
Vol 04 (03) ◽  
pp. 481-494 ◽  
Author(s):  
S. Ramkumar ◽  
C. Ganesa Moorthy
Keyword(s):  
Hausdorff Compactifications

A construction for all Hausdorff compactifications given in the article [2] is analysed further to obtain other topological extensions, namely, regular extensions and normal extensions. The method is also applied to derive and to study convex compactifications.

scholarly journals On largest Hausdorff compactification for convergence spaces

1975 ◽  
Vol 12 (1) ◽  
pp. 73-79 ◽  
Author(s):  
C.J.M. Rao
Keyword(s):  
Convergence Spaces ◽  
Hausdorff Compactifications

In this note we obtain a characterization of the class of convergence spaces for which Richardson's compactification is the largest Hausdorff compactification and a characterization of the class of convergence spaces which possess largest Hausdorff compactifications.

scholarly journals On Hausdorff compactifications of non-locally compact spaces

1979 ◽  
Vol 2 (3) ◽  
pp. 481-486
Author(s):  
James Hatzenbuhler ◽  
Don A. Mattson
Keyword(s):  
Hausdorff Space ◽  
Locally Compact ◽  
Completely Regular ◽  
Compact Spaces ◽  
Hausdorff Compactifications ◽  
Set Of Points ◽  
Locally Compact Spaces

LetXbe a completely regular, Hausdorff space and letRbe the set of points inXwhich do not possess compact neighborhoods. AssumeRis compact. IfXhas a compactification with a countable remainder, then so does the quotientX/R, and a countable compactificatlon ofX/Rimplies one forX−R. A characterization of whenX/Rhas a compactification with a countable remainder is obtained. Examples show that the above implications cannot be reversed.

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