[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c200443

𝜇-COUNTABLY COMPACTNESS AND 𝜇𝓗-COUNTABLY COMPACTNESS

Altawallbeh, Zuhier (Department of Mathematics Tafila Technical University)
Jawarneh, Ibrahim (Department of Mathematics Al-Hussein Bin Talal University)

Publication Information

Communications of the Korean Mathematical Society / v.37, no.1, 2022 , pp. 269-277 More about this Journal

Abstract

We define and study the notion of 𝜇-countably compact spaces in generalized topology and 𝜇𝓗-countably compact spaces which are considered with respect to a hereditary class 𝓗. Some interesting properties and relations are provided in the paper. Moreover, some preservation of functions properties are studied and investigated.

Keywords

${\mu}$ -countably compactness; ${\mu}{\mathcal{H}}$ -countably compactness;

Citations & Related Records

Reference

1	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 DOI
2	A. Csaszar, 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 DOI
3	A. Csaszar, 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 DOI
4	Z. Altawallbeh, More on almost countably compact spaces, Italian J. Pure Appl. Math. 43 (2020), 177-184.
5	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
6	A. Csaszar, Generalized topology, generalized continuity, Acta Math. Hungar. 96 (2002), no. 4, 351-357. https://doi.org/10.1023/A:1019713018007 DOI
7	A. Csaszar, Weak structures, Acta Math. Hungar. 131 (2011), no. 1-2, 193-195. https://doi.org/10.1007/s10474-010-0020-z DOI
8	A. Qahis, H. H. AlJarrah, and T. Noiri, µ-Lindelofness in terms of a hereditary class, Missouri J. Math. Sci. 28 (2016), no. 1, 15-24. http://projecteuclid.org/euclid.mjms/1474295352
9	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 DOI
10	A. Pavlovic, Local function versus local closure function in ideal topological spaces, Filomat 30 (2016), no. 14, 3725-3731. https://doi.org/10.2298/FIL1614725P DOI
11	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 DOI
12	M. S. Sarsak, Weakly µ-compact spaces, Demonstratio Math. 45 (2012), no. 4, 929-938. DOI
13	A. M. Zahran, K. El-Saady, and A. Ghareeb, Modification of weak structures via hereditary classes, Appl. Math. Lett. 25 (2012), no. 5, 869-872. https://doi.org/10.1016/j.aml.2011.10.034 DOI
14	K. Kuratowski, Topologie, Warszawa. I (1933).