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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.
Axioms 2019, 8(1), 33; https://doi.org/10.3390/axioms8010033
Received: 9 February 2019 / Revised: 6 March 2019 / Accepted: 8 March 2019 / Published: 14 March 2019
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
MDPI and ACS Style

Banakh, T.; Protasov, I. Functional Boundedness of Balleans: Coarse Versions of Compactness. Axioms 2019, 8, 33.

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