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HOMOGENEOUS FUNCTIONALLY ALEXANDROFF SPACES

Part of: Generalities Lattices Maps and general types of spaces defined by maps

Published online by Cambridge University Press:  08 November 2017

SAMI LAZAAR Open the ORCID record for SAMI LAZAAR [Opens in a new window] ,
TOM RICHMOND Open the ORCID record for TOM RICHMOND [Opens in a new window]  and
HOUSSEM SABRI Open the ORCID record for HOUSSEM SABRI [Opens in a new window]
SAMI LAZAAR
Affiliation:
Department of Mathematics, Faculty of Sciences of Gafsa, University of Gafsa, Tunisia email salazaar72@yahoo.fr
TOM RICHMOND*
Affiliation:
Department of Mathematics, Western Kentucky University, Bowling Green, KY 42104, USA email tom.richmond@wku.edu
HOUSSEM SABRI
Affiliation:
Department of Mathematics, Faculty of Science of Tunis, University of Tunis El Manar, Tunisia email sabrihoussem@gmail.com
*
✉tom.richmond@wku.edu
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Abstract

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A function $f:X\rightarrow X$ determines a topology $P(f)$ on $X$ by taking the closed sets to be those sets $A\subseteq X$ with $f(A)\subseteq A$. The topological space $(X,P(f))$ is called a functionally Alexandroff space. We completely characterise the homogeneous functionally Alexandroff spaces.

Keywords

functionally Alexandroff spacehomogeneous spacespecialisation

MSC classification

Primary: 54C99: None of the above, but in this section
Secondary: 54A05: Topological spaces and generalizations (closure spaces, etc.) 06B30: Topological lattices, order topologies
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 2 , April 2018 , pp. 331 - 339
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

The first author acknowledges the support of the research laboratory LATAO (grant LR11ES16).

References

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