A generalization of connectedness via ideals
DOI:
https://doi.org/10.52737/18291163-2022.14.7-1-18Keywords:
Connectedness, ideal topological spacesAbstract
In this paper, we define and study the $\diamond$-connected spaces as a generalization of the connectedness, and thus of the Ekici-Noiri and Modak-Noiri notions, through ideals.
References
E. Ekici and T. Noiri, ⋆-hyperconnected ideal topological spaces, Annals of the Alexandru Ioan Cuza University - Mathematics, 58 (2012), pp. 121-129. https://doi.org/10.2478/v10157-011-0045-9
D. Jancović and T.R. Hamlett, Compatible extensions of ideals, Boll. Un. Math Ita. B (7), 6 (1992), no 3, pp. 453-465.
D. Jancović and T.R. Hamlett, New topologies from old via ideals, Am. Math. Mon., 97 (1990), no 4, pp. 295-310. https://doi.org/10.1080/00029890.1990.11995593
K. Kuratowski, Topology, vol. I, Academic Press, New York, 1966.
R.L. Newcomb, Topologies which are compact modulo an ideal, Ph. Dissertation, Univ. of California at Santa Barbara, 1967.
N.R. Pachón Rubiano, Between closed and I_g-closed sets, Eur. J. Pure Applied Math., 11 (2018), no 1, pp. 299-314. https://doi.org/10.29020/nybg.ejpam.v11i2.3131
S. Modak and T. Noiri, A weaker form of connectedness, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 65 (2016), no 1, pp. 49-52. https://doi.org/10.1501/Commua1_0000000743
S. Modak and T. Noiri, Connectedness of ideal topological spaces, Filomat, 29 (2015), no 4, pp. 661-665. https://doi.org/10.2298/FIL1504661M
R. Vaidyanathaswamy, The localisation theory in set-topology, Proc. Indian Acad. Sci. A, 20 (1944), no 1, pp. 51-61. https://doi.org/10.1007/BF03048958
S. Willard, General Topology, Dover Publications, Inc., 2004.
Downloads
Published
Issue
Section
License
Copyright (c) 2022 Armenian Journal of Mathematics
This work is licensed under a Creative Commons Attribution 4.0 International License.
