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\(\mu\)-countably compactness and \(\mu\mathcal{H}\)-countably compactness.(English)Zbl 1484.54002

Summary: We define and study the notion of \(\mu\)-countably compact spaces in generalized topology and \(\mu\mathcal{H}\)-countably compact spaces which are considered with respect to a hereditary class \(\mathcal{H}\). Some interesting properties and relations are provided in the paper. Moreover, some preservation of functions properties are studied and investigated.

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
54D30 Compactness

Cite

References:

[1]Z. Altawallbeh, More on almost countably compact spaces, Italian J. Pure Appl. Math. 43 (2020), 177-184.
[2]Z. Altawallbeh and A. Al-Momany, Nearly countably compact spaces, Int. Electron. J. Pure Appl. Math. 8 (2014), no. 4, 59-66. https://doi.org/10.12732/iejpam.v8i4.7 ·doi:10.12732/iejpam.v8i4.7
[3]C. Carpintero, E. Rosas, M. Salas-Brown, and J. Sanabria, µ-compactness with respect to a hereditary class, Bol. Soc. Parana. Mat. (3) 34 (2016), no. 2, 231-236. https: //doi.org/10.5269/bspm.v34i2.27177 ·Zbl 1424.54054 ·doi:10.5269/bspm.v34i2.27177
[4]Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), no. 4, 351-357. https://doi.org/10.1023/A:1019713018007 ·Zbl 1006.54003 ·doi:10.1023/A:1019713018007
[5]Á. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar. 106 (2005), no. 1-2, 53-66. https://doi.org/10.1007/s10474-005-0005-5 ·Zbl 1076.54500 ·doi:10.1007/s10474-005-0005-5
[6]Á. Császár, Modification of generalized topologies via hereditary classes, Acta Math. Hungar. 115 (2007), no. 1-2, 29-36. https://doi.org/10.1007/s10474-006-0531-9 ·Zbl 1135.54300 ·doi:10.1007/s10474-006-0531-9
[7]Á. Császár, Weak structures, Acta Math. Hungar. 131 (2011), no. 1-2, 193-195. https: //doi.org/10.1007/s10474-010-0020-z ·Zbl 1240.54004 ·doi:10.1007/s10474-010-0020-z
[8]K. Kuratowski, Topologie, Warszawa. I (1933).
[9]A. Pavlović, Local function versus local closure function in ideal topological spaces, Filomat 30 (2016), no. 14, 3725-3731. https://doi.org/10.2298/FIL1614725P ·Zbl 1461.54016 ·doi:10.2298/FIL1614725P
[10]A. Qahis, H. H. AlJarrah, and T. Noiri, µ-Lindelöfness in terms of a hereditary class, Missouri J. Math. Sci. 28 (2016), no. 1, 15-24. http://projecteuclid.org/euclid. mjms/1474295352 ·Zbl 1393.54012
[11]L. E. de Arruda Saraiva, Generalized quotient topologies, Acta Math. Hungar. 132 (2011), no. 1-2, 168-173. https://doi.org/10.1007/s10474-010-0047-1 ·Zbl 1249.54002 ·doi:10.1007/s10474-010-0047-1
[12]M. S. Sarsak, Weak separation axioms in generalized topological spaces, Acta Math. Hungar. 131 (2011), no. 1-2, 110-121. https://doi.org/10.1007/s10474-010-0017-7 ·Zbl 1274.54009 ·doi:10.1007/s10474-010-0017-7
[13]M. S. Sarsak, Weakly µ-compact spaces, Demonstratio Math. 45 (2012), no. 4, 929-938. ·Zbl 1272.54003
[14]A. M. Zahran, K. El-Saady, and A. Ghareeb, Modification of weak structures via hered-itary classes, Appl. Math. Lett. 25 (2012), no. 5, 869-872. https://doi.org/10.1016/ j.aml.2011.10.034 ·Zbl 1241.54001 ·doi:10.1016/j.aml.2011.10.034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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