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Georgian Mathematical Journal

Editor-in-Chief: Kiguradze, Ivan / Buchukuri, T.

Editorial Board: Kvinikadze, M. / Bantsuri, R. / Baues, Hans-Joachim / Besov, O.V. / Bojarski, B. / Duduchava, R. / Engelbert, Hans-Jürgen / Gamkrelidze, R. / Gubeladze, J. / Hirzebruch, F. / Inassaridze, Hvedri / Jibladze, M. / Kadeishvili, T. / Kegel, Otto H. / Kharazishvili, Alexander / Kharibegashvili, S. / Khmaladze, E. / Kiguradze, Tariel / Kokilashvili, V. / Krushkal, S. I. / Kurzweil, J. / Kwapien, S. / Lerche, Hans Rudolf / Mawhin, Jean / Ricci, P.E. / Tarieladze, V. / Triebel, Hans / Vakhania, N. / Zanolin, Fabio


IMPACT FACTOR 2018: 0.551

CiteScore 2018: 0.52

SCImago Journal Rank (SJR) 2018: 0.320
Source Normalized Impact per Paper (SNIP) 2018: 0.711

Mathematical Citation Quotient (MCQ) 2018: 0.27

Online
ISSN
1572-9176
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Volume 26, Issue 2

Issues

An example of a hereditarily normal topologically finite space, which is topologically infinite relative to the class of all its proper F σ-subspaces

Ivane Tsereteli
Published Online: 2019-04-06 | DOI: https://doi.org/10.1515/gmj-2019-2014

Abstract

A (Hausdorf) hereditarily normal (not perfectly normal) space X is constructed, which has the following properties: (a) there exists a proper open subspace of X which is homeomorphic to the whole X (i.e., the space X is topologically infinite); (b) the space is homeomorphic to none of its proper Fσ-subspaces (i.e., the space X is topologically finite relative to the class of all its proper Fσ-subspaces).

Keywords: Topologically finite; relative; long line

MSC 2010: 54F45

Dedicated to Academician Nodar Berikashvili on the occasion of his 90th birthday

References

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    I. Tsereteli, Topological finiteness, Bernstein sets, and topological rigidity, Topology Appl. 159 (2012), no. 6, 1645–1653. Web of ScienceCrossrefGoogle Scholar

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    I. Tsereteli, Relative topological finiteness, Georgian Math. J. 22 (2015), no. 4, 573–579. Web of ScienceGoogle Scholar

About the article

Received: 2017-09-05

Accepted: 2018-10-03

Published Online: 2019-04-06

Published in Print: 2019-06-01


Citation Information: Georgian Mathematical Journal, Volume 26, Issue 2, Pages 315–319, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2019-2014.

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