×

A note on generalized connectedness. (English) Zbl 1265.54021

Summary: This note is devoted to studying the preservation of connectedness under the basic operators in generalized topological spaces. Some characterizations of generalized connectedness are given. As an application, we generalize some results in topological spaces.

MSC:

54A05 Topological spaces and generalizations (closure spaces, etc.)
54D15 Higher separation axioms (completely regular, normal, perfectly or collectionwise normal, etc.)
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] T. Aho and T. Nieminen, Spaces in which preopen subsets are semi-open, Ricerche Mat., 43 (1994), 45–59. · Zbl 0912.54030
[2] Á. Császár, Generalized open sets, Acta Math. Hungar., 75 (1979), 65–87. · Zbl 0924.54003
[3] Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351–357. · Zbl 1006.54003
[4] Á. Császár, {\(\gamma\)}-connected sets, Acta Math. Hungar., 101 (2003), 273–279. · Zbl 1049.54021
[5] Á. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar., 106 (2005), 53–66. · Zbl 1076.54500
[6] Z. Duszyński, On some concepts of weak connectdness of topological spaces, Acta Math. Hungar., 110 (2006), 81–90. · Zbl 1120.54311
[7] V. Pipitone and G. Russo, Spazi semiconnessi e spazi semiaperti, Rend. Circ. Mat. Palermo, 24 (1975), 273–285.
[8] V. Popa, Properties of H-almost continuous functions, Bull. Math. Soc. Sci. Math. R.S. Roumanie (N.S.), 79 (1987), 163–168. · Zbl 0618.54013
[9] V. Popa and T. Noiri, Weakly {\(\beta\)}-continuous functions, An. Univ. Timisoara Ser. Mat. Inform., 32 (1994), 83–92. · Zbl 0864.54009
[10] T. Thompson, Characterizations of irreducible space, Kyungpook Math. J., 21 (1981), 191–194. · Zbl 0529.54010
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.