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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

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SCImago Journal Rank (SJR) 2018: 0.320
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Volume 26, Issue 2


Finite spaces and an axiomatization of the Lefschetz number

Paweł Bilski
  • Corresponding author
  • Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-656 Warsaw, Poland
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Published Online: 2017-05-11 | DOI: https://doi.org/10.1515/gmj-2017-0012


In [1] Arkowitz and Brown presented an axiomatization of the reduced Lefschetz number of self-maps of finite CW-complexes. By the results of McCord [8], finite simplicial complexes are closely related to finite T0-spaces. This connection and the axioms given by Arkowitz and Brown suggest an axiomatization of the reduced Lefschetz number of maps of finite T0-spaces. However, using the notion of the subdivision of a finite T0-space, we consider the degree and the Lefschetz number of not only self-maps. We also present some properties of the degree of maps between finite models of the circle 𝕊1.

Keywords: Euler characteristic; finite topological spaces; Lefschetz number

MSC 2010: 54H25; 55M20


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About the article

Received: 2015-02-12

Revised: 2015-08-02

Accepted: 2015-10-23

Published Online: 2017-05-11

Published in Print: 2019-06-01

Citation Information: Georgian Mathematical Journal, Volume 26, Issue 2, Pages 165–175, ISSN (Online) 1572-9176, ISSN (Print) 1072-947X, DOI: https://doi.org/10.1515/gmj-2017-0012.

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