Abstract
In this paper, we characterize spaces such that their one-point compactification (resp., Herrlich compactification) is weakly submaximal. We also establish a necessary and sufficient condition on \(T_{0}\)-spaces in order to get their one-point compactification (resp., Herrlich compactification) \(T_{D}\)-spaces.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Arhangel’skii, A.V.; Collins, P.J.: On submaximal spaces. Topol. Appl. 64, 219–241 (1995)
Belaid, K.; Dridi, L.; Echi, O.: Submaximal spaces and door compactifications. Topol. Appl. 158, 1969–1975 (2011)
Bouacida, E.; Echi, O.; Salhi, E.: Topologies associée à une relation binaire et relation binaire spéciale. Boll. Unione Mat. Italiana 7(10), 417–439 (1996)
Dontchev, J.: On submaximal spaces. Tamkang J. Math. 26, 243–250 (1995)
Herrlich, H.: Compact \(T_{0}\)-spaces and \(T_{0}\)-compactifications. Appl. Categ. Struct. 1, 111–132 (1993)
Kenndy, G.J.; Mccartan, S.D.: Minimal weakly supmaximal topology. Math. Proc. R. Irish Acad. 2, 133–140 (1999)
Levy, R.; Porter, J.R.: On two questions of Arhangel’skii and Collins regarding submaximal spaces. Topol. Proc. 21, 143–154 (1966)
Lewis, W.J.; Ohm, J.: The ordering of spec R. Can. J. Math. 28, 820–835 (1976)
Schröder, J.: Some answers concerning submaximal spaces. Quest. Answ. Gen. Topol. 17, 221–225 (1999)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Hajri, M.A., Belaid, K. & Belaid, L.J. Weakly submaximal spaces and compactifications. Arab. J. Math. 6, 257–261 (2017). https://doi.org/10.1007/s40065-017-0176-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40065-017-0176-2