About Compactness Type of Uniform Spaces
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Authors: D. KANETOVA AND B. KANETOV
DOI: 10.46793/KgJMat2609.1425K
Abstract:
This paper introduces uniform analogues of compact, finally compact and countable compact spaces and investigates their connection with other uniform properties of compactness type.
Keywords:
Compactness, u-uniformly compactness, u-uniformly finally compactness, u-uniformly countable compactness.
References:
[1] A. A. Borubaev, Uniform Topology, Bishkek, Ilim, 2013.
[2] A. A. Borubaev, B. E. Kanetov, A. M. Baidzhuranova, T. Zh. Zhumaliev and A. Bekbolsunova, On the R-compactification of uniform spaces, AIP Conference Proceedings 2879 (2023), Article ID 020001. https://doi.org/10.1063/5.0175194
[3] Lj. D. R. Kočinac, Selection principles in uniform spaces, Note di Mathematica 22 (2003), 127–139.
[4] B. E. Kanetov, Some Classes of Uniform Spaces and Uniformly Continuous Mappings, Bishkek, KNU, 2013.
[5] B. E. Kanetov and N. A. Baigazieva, Strong uniform paracompactness, AIP Conference Proceedings 1997 (2018), Article ID 020085. https://doi.org/10.1063/1.5049079
[6] B. E. Kanetov, A. M. Baidzhuranova and B. A. Almazbekova, About weakly uniformly paracompact spaces, AIP Conference Proceedings 2483 (2022), Article ID 020004. https://doi.org/10.1063/5.0129289
[7] B. E. Kanetov, U. A. Saktanov and D. E. Kanetova, Some remainders properties of uniform spaces and uniformly continuous mappings, AIP Conference Proceedings 2183 (2019), Article ID 030011. https://doi.org/10.1063/1.5136115
[8] B. E. Kanetov, D. E. Kanetova and M. O. Zhanakunova, On some completeness properties of uniform spaces, AIP Conference Proceedings 2183 (2019), Article ID 030010. https://doi.org/10.1063/5136114
[9] B. E. Kanetov, N. A. Baigazieva and N. I. Altybaev, About uniformly-paracompact spaces, Int. J. Appl. Math. 34 (2021), 353–362. https://dx.doi.org/10.12732/ijam.v34i2.11
[10] B. E. Kanetov and A. M. Baidzhuranova, Paracompact-type mappings, Bulletin of the Karaganda University. Mathematics Series 2 (2021), 62–66. https://doi.org/10.31489/2021M2/67-73
[11] B. E. Kanetov and A. M. Baidzhuranova, On a uniform analogue of paracompact spaces, AIP Conference Proceedings 2183 (2019), Article ID 030009. https://doi.org/10.1063/1.5136113
[12] B. E. Kanetov, D. E. Kanetova and N. I. Altybaev, On countably uniformly paracompact spaces, AIP Conference Proceedings 2334 (2020), Article ID 020011. https://doi.org/10.1063/5.0046213
[13] B. E. Kanetov, U. A. Saktanov and A. M. Baidzhuranova, Totally bounded remainders of uniform spaces and samuel compactification of uniformly continuous mappings, AIP Conference Proceedings 2334 (2021), Article ID 020013. https://doi.org/10.1063/5.0046220
[14] B. E. Kanetov, D. E. Kanetova and A. M. Baidzhuranova, About uniformly Menger spaces, Mathematica Moravika 28 (2024), 53–61. https://doi.org/10.5937/MatMor23401053K
[15] B. E. Kanetov, D. E. Kanetova and M. K. Beknazarova, About uniform analogues of strongly paracompact and Lindelöf spaces, Trans. Natl. Acad. Sci. Azerb. Ser. Phys.-Tech. Math. Sci. 44 (2024), 117–127. https://doi.org/10.30546/2617-7900.44.1.2024.117
