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.

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 Two extensions of the stone duality to the category of zero-dimensional Hausdorff spaces

Filomat ◽  
2021 ◽  
Vol 35 (6) ◽  
pp. 1851-1878
Author(s):  
Georgi Dimov ◽  
Elza Ivanova-Dimova
Keyword(s):  
Duality Theorem ◽  
Hausdorff Space ◽  
Stone Duality ◽  
Hausdorff Spaces ◽  
Duality Theorems ◽  
Extremally Disconnected ◽  
Continuous Maps ◽  
Hausdorff Compactifications ◽  
Tychonoff Spaces

Extending the Stone Duality Theorem, we prove two duality theorems for the category ZHaus of zero-dimensional Hausdorff spaces and continuous maps. They extend also the Tarski Duality Theorem; the latter is even derived from one of them. We prove as well two new duality theorems for the category EDTych of extremally disconnected Tychonoff spaces and continuous maps. Also, we describe two categories which are dually equivalent to the category ZComp of zero-dimensional Hausdorff compactifications of zero-dimensional Hausdorff spaces and obtain as a corollary the Dwinger Theorem about zero-dimensional compactifications of a zero-dimensional Hausdorff space.

On 𝒞ℛ-Epic Embeddings and Absolute 𝒞ℛ-Epic Spaces

2005 ◽  
Vol 57 (6) ◽  
pp. 1121-1138 ◽  
Author(s):  
Michael Barr ◽  
R. Raphael ◽  
R. G. Woods
Keyword(s):  
Locally Compact ◽  
Compact Spaces ◽  
Open Questions ◽  
Tychonoff Spaces ◽  
Locally Compact Spaces

AbstractWe study Tychonoff spaces X with the property that, for all topological embeddings X → Y, the induced map C(Y ) → C(X) is an epimorphism of rings. Such spaces are called absolute 𝒞ℛ-epic. The simplest examples of absolute 𝒞ℛ-epic spaces are σ-compact locally compact spaces and Lindelöf P-spaces. We show that absolute CR-epic first countable spaces must be locally compact.However, a “bad” class of absolute CR-epic spaces is exhibited whose pathology settles, in the negative, a number of open questions. Spaces which are not absolute CR-epic abound, and some are presented.

scholarly journals Bounded resolutions for spaces $$C_{p}(X)$$ and a characterization in terms of X

2021 ◽  
Vol 115 (2) ◽  
Author(s):  
J. C. Ferrando ◽  
J. Ka̧kol ◽  
W. Śliwa
Keyword(s):  
Tychonoff Space ◽  
Cosmic Space ◽  
Tychonoff Spaces

AbstractAn internal characterization of the Arkhangel’skiĭ-Calbrix main theorem from [4] is obtained by showing that the space $$C_{p}(X)$$ C p ( X ) of continuous real-valued functions on a Tychonoff space X is K-analytic framed in $$\mathbb {R}^{X}$$ R X if and only if X admits a nice framing. This applies to show that a metrizable (or cosmic) space X is $$\sigma $$ σ -compact if and only if X has a nice framing. We analyse a few concepts which are useful while studying nice framings. For example, a class of Tychonoff spaces X containing strictly Lindelöf Čech-complete spaces is introduced for which a variant of Arkhangel’skiĭ-Calbrix theorem for $$\sigma $$ σ -boundedness of X is shown.

Two-Dimension-Like Functions Defined on the Class of all Tychonoff Spaces

1995 ◽  
Vol 2 (2) ◽  
pp. 201-210
Author(s):  
I. Tsereteli
Keyword(s):  
Two Dimension ◽  
Dimension Functions ◽  
Tychonoff Spaces

Abstract Two-dimension-like functions are constructed on the class of all Tychonoff spaces. Several of their properties, analogous to those of the classical dimension functions, are established.

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.

scholarly journals On compactification of mappings

1974 ◽  
Vol 19 (2) ◽  
pp. 105-108
Author(s):  
P. A. Firby
Keyword(s):  
Continuous Function ◽  
Dense Subspace ◽  
Compact Extension ◽  
Tychonoff Spaces ◽  
Function Mapping

If X and Y are Tychonoff spaces then the continuous function f mapping X onto Y is said to be compact (perfect, or proper) if it is closed and point inverses are compact. If h is a continuous function mapping X onto Y then by a compactification of h we mean a pair (X*, h*) where X* is Tychonoff and contains X as a dense subspace, and where h*: X*→Y is a compact extension of h. The idea of a mapping compactification first appeared in (7). In (1) it was shown that any compactification of X determines a compactification of h, and that any compactification of h can be determined in this way. This idea was then developed in (2) and (3).

Hausdorff compactifications in ZF

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