AP-space and an extremally disconnected space whose product is not anF-space

1960 ◽  
Vol 11 (1) ◽  
pp. 53-55 ◽  
Author(s):  
Leonard Gillman
Keyword(s):  
Extremally Disconnected ◽  
Extremally Disconnected Space

scholarly journals Disconnection in the Alexandroff duplicate

2021 ◽  
Vol 22 (2) ◽  
pp. 331
Author(s):  
Papiya Bhattacharjee ◽  
Michelle L. Knox ◽  
Warren Wm. McGovern
Keyword(s):  
Extremally Disconnected ◽  
Extremally Disconnected Space

<p>It was demonstrated in [2] that the Alexandroff duplicate of the Čech-Stone compactification of the naturals is not extremally disconnected. The question was raised as to whether the Alexandroff duplicate of a non-discrete extremally disconnected space can ever be extremally disconnected. We answer this question in the affirmative; an example of van Douwen is significant. In a slightly different direction we also characterize when the Alexandroff duplicate of a space is a P-space as well as when it is an almost P-space.</p>

Co-Absolutes with Homeomorphic Dense Subspaces

1981 ◽  
Vol 33 (4) ◽  
pp. 857-861
Author(s):  
Scott W. Williams
Keyword(s):  
Regular Space ◽  
Complete Space ◽  
Completely Regular ◽  
Extremally Disconnected ◽  
Ordered Space ◽  
Extremally Disconnected Space ◽  
Dense Sets

Recall that the absolute ∈(X) of a regular space X is the unique (up to a homeomorphism) extremally disconnected space whose image is X under a perfect irreducible map. X and Y are co-absolute whenever ∈(X) and ∈(Y) are homeomorphic. Completely regular spaces X and Y are weakly co-absolute whenever βX and βY are co-absolute. For a survey of this area we suggest [6] and [8].In this paper we proveTHEOREM 1. Suppose, for i ∈ {0, 1};, X(i) is a compact connected linearly ordered space. Then X(0) and X(l) are co-absolute if, and only if, X(0) and X(l) have homeomorphic dense sets.Making use of Theorem 1 and a result from [7] we give Theorem 2, a cardinal generalization ofCOROLLARY 1. Suppose for each i ∈ {0, 1};, X(i) is a Čech-complete space with a Gδ-diagonal.

scholarly journals £-Single Valued Extremally Disconnected Ideal Neutrosophic Topological Spaces

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 53
Author(s):  
Fahad Alsharari
Keyword(s):  
Topological Spaces ◽  
Neutrosophic Sets ◽  
Extremally Disconnected ◽  
Fundamental Properties ◽  
Separation Axioms ◽  
New Concepts ◽  
Definition Of

This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-Ri (r-SVNIRi, for short), where i={0,1,2,3}, and r-single valued neutrosophic ideal-Tj (r-SVNITj, for short), where j={1,2,212,3,4}, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied.

Projective Elements in Categories with Perfect θ-Continuous Maps

1981 ◽  
Vol 33 (4) ◽  
pp. 872-884 ◽  
Author(s):  
Hans Vermeer ◽  
Evert Wattel
Keyword(s):  
Hausdorff Space ◽  
Continuous Functions ◽  
List Type ◽  
Hausdorff Spaces ◽  
Extremally Disconnected ◽  
Continuous Maps

In 1958 Gleason [6] proved the following :THEOREM. In the category of compact Hausdorff spaces and continuous maps, the projective elements are precisely the extremally disconnected spaces.The projective elements in many topological categories with perfect continuous functions as morphisms have been found since that time. For example: In the following categories the projective elements are precisely the extremally disconnected spaces:(i) The category of Tychonov spaces and perfect continuous functions. [4] [11].(ii) The category of regular spaces and perfect continuous functions. [4] [12].(iii) The category of Hausdorff spaces and perfect continuous functions. [10] [1].(iv) In the category of Hausdorff spaces and continuous k-maps the projective members are precisely the extremally disconnected k-spaces. [14].In 1963 Iliadis [7] constructed for every Hausdorff space X the so called Iliadis absolute E[X], which is a maximal pre-image of X under irreducible θ-continuous maps.

CHARACTERIZATIONS OF L-EXTREMALLY DISCONNECTED SPACES

2007 ◽  
pp. 1252-1258
Author(s):  
Ji-Shu Cheng ◽  
Shui-Li Chen
Keyword(s):  
Extremally Disconnected

Complemented ideals and extremally disconnected spaces

1961 ◽  
Vol 12 (1) ◽  
pp. 349-354 ◽  
Author(s):  
D. G. Johnson ◽  
J. E. Kist
Keyword(s):  
Extremally Disconnected

scholarly journals Projective bitopological spaces II.

1972 ◽  
Vol 14 (1) ◽  
pp. 119-128 ◽  
Author(s):  
M. C. Datta
Keyword(s):  
Full Subcategory ◽  
Hausdorff Spaces ◽  
Extremally Disconnected ◽  
Continuous Maps ◽  
Bitopological Spaces ◽  
Perfect Maps

Gleason [3] proved that in the category G of compact Hausdorff spaces and continuous maps, the projective objects are precisely the extremally disconnected spaces contained in the category. Strauss [7] generalised this and proved that in the category G of regular Hausdorif spaces and perfect maps the projective objects are again precisely the extremally disconnected ones. Observe that Gleason's category is a full subcategory of Strauss's category.

scholarly journals rc-continuous functions and functions with rc-strongly closed graph

2003 ◽  
Vol 2003 (72) ◽  
pp. 4547-4555
Author(s):  
Bassam Al-Nashef
Keyword(s):  
Continuous Function ◽  
Topological Space ◽  
Continuous Functions ◽  
Closed Graph ◽  
Compact Spaces ◽  
Extremally Disconnected ◽  
The Family ◽  
Regular Closed

The family of regular closed subsets of a topological space is used to introduce two concepts concerning a functionffrom a spaceXto a spaceY. The first of them is the notion offbeing rc-continuous. One of the established results states that a spaceYis extremally disconnected if and only if each continuous function from a spaceXtoYis rc-continuous. The second concept studied is the notion of a functionfhaving an rc-strongly closed graph. Also one of the established results characterizes rc-compact spaces (≡S-closed spaces) in terms of functions that possess rc-strongly closed graph.

scholarly journals On extremally disconnected topological groups

2006 ◽  
Vol 153 (14) ◽  
pp. 2382-2385 ◽  
Author(s):  
Yevhen Zelenyuk
Keyword(s):  
Topological Groups ◽  
Extremally Disconnected

A note on mappings of extremally disconnected spaces

1985 ◽  
Vol 46 (1-2) ◽  
pp. 83-92 ◽  
Author(s):  
D. S. Janković
Keyword(s):  
Extremally Disconnected
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