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Nonhomogeneity of remainders


Authors: A. V. Arhangel’skii and J. van Mill
Journal: Proc. Amer. Math. Soc. 144 (2016), 4065-4073
MSC (2010): Primary 54D35, 54D40, 54A25
DOI: https://doi.org/10.1090/proc/13172
Published electronically: April 27, 2016
MathSciNet review: 3513561
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Abstract: We present a cardinal inequality for the number of homeomorphisms of the remainders of compactifications of nowhere locally compact spaces. As a consequence, we obtain that if $ X$ is countable and dense in itself, then the remainder of any compactification of $ X$ has at most continuum many homeomorphisms.


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Additional Information

A. V. Arhangel’skii
Affiliation: Moscow State University and Moscow State Pedagogical University, Moscow, Russia
Email: arhangel.alex@gmail.com

J. van Mill
Affiliation: KdV Institute for Mathematics, University of Amsterdam, Science Park 904, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands
Email: j.vanMill@uva.nl

DOI: https://doi.org/10.1090/proc/13172
Keywords: Remainder, compactification, topological group, homogeneous space, first-countable, Continuum Hypothesis, Martin's Axiom
Received by editor(s): May 15, 2015
Received by editor(s) in revised form: May 19, 2015, and September 21, 2015
Published electronically: April 27, 2016
Additional Notes: The work of the first-named author is supported by RFBR, project 15-01-05369
Communicated by: Mirna Džamonja
Article copyright: © Copyright 2016 American Mathematical Society