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Axioms 2019, 8(1), 33; https://doi.org/10.3390/axioms8010033

Functional Boundedness of Balleans: Coarse Versions of Compactness

1
Faculty of Mechanics and Mathematics, Ivan Franko National University of Lviv, Universytetska, 79000 Lviv, Ukraine
2
Institute of Mathematics, Jan Kochanowski University, Świȩtokrzyska 15, 25-406 Kielce, Poland
3
Faculty of Cybernetics, Taras Shevchenko National University, Glushkov avenue 4d, 03680 Kyiv, Ukraine
*
Author to whom correspondence should be addressed.
Received: 9 February 2019 / Revised: 6 March 2019 / Accepted: 8 March 2019 / Published: 14 March 2019
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PDF [306 KB, uploaded 14 March 2019]

Abstract

We survey some results and pose some open problems related to boundedness of real-valued functions on balleans and coarse spaces. Special attention is paid to balleans on groups. The boundedness of functions that respect the coarse structure of a ballean could be considered as a coarse counterpart of pseudo-compactness. View Full-Text
Keywords: coarse structure; ballean; group; real-valued function; boundedness coarse structure; ballean; group; real-valued function; boundedness
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Banakh, T.; Protasov, I. Functional Boundedness of Balleans: Coarse Versions of Compactness. Axioms 2019, 8, 33.

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