Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-24T13:05:35.340Z Has data issue: false hasContentIssue false
  • English
  • Français

On semi-regularization topologies

Part of: Fairly general properties Maps and general types of spaces defined by maps Generalities

Published online by Cambridge University Press:  09 April 2009

M. Mršević ,
I. L. Reilly  and
M. K. Vamanamurthy
M. Mršević
Affiliation:
Institute of Mathematics Faculty of Sciences University of Belgrade, Yugoslavia
I. L. Reilly
Affiliation:
Department of Mathematics & Statistics University of Auckland, New Zealand
M. K. Vamanamurthy
Affiliation:
Department of Mathematics & Statistics University of Auckland, New Zealand
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

This paper discusses several properties of topological spaces and how they are refelected by corresponding properties of the associated semi-regularization topologies. For example a space is almost locally connected if and only if its semi-regularization is locally connected. Various separation, connectedness, covering, and mapping properties are considered.

Keywords

semi-regularregular openalmost regularalmost locally connectednearly compactalmost continuousδ-continuoussuper-constinuous.

MSC classification

Secondary: 54A10: Several topologies on one set (change of topology, comparison of topologies, lattices of topologies) 54C10: Special maps on topological spaces (open, closed, perfect, etc.) 54D05: Connected and locally connected spaces (general aspects) 54D10: Lower separation axioms ($T_0$--$T_3$, etc.) 54D30: Compactness
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 38 , Issue 1 , February 1985 , pp. 40 - 54
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Bourbaki, N., Elements of mathematics. General topology. Part I. (Herman, Paris; Addison-Wesley, Reading, Mass., 1966).Google Scholar
[2]Cameron, D. E., ‘Properties of S-closed spaces’, Proc. Amer. Math. Soc. 72 (1978), 581–586.Google Scholar
[3]Carnahan, D., ‘Locally nearly compact spaces’, Boll. Un. Mat. Ital. (4) 6 (1972), 14–153.Google Scholar
[4]Crossley, S. G., ‘A note on semi topological properties’, Proc. Amer. Math. Soc. 72 (1978), 409–412.Google Scholar
[5]Dugundji, J., Topology (Allyn and Bacon, Boston, Mass., 1966).Google Scholar
[6]Herrington, L. L., ‘Properties of nearly compact spaces’, Proc. Amer. Math. Soc. 45 (1974), 431–436.Google Scholar
[7]Herrington, L. L., ‘Characterizations of Urysohn-closed spaces’, Proc. Amer. Math. Soc. 55 (1976), 435–439.Google Scholar
[8]Hemnan, R. A., ‘Nearly compact Hausdorff extensions’, Glasnik Mat. 12 (32), (1977), 125–132.Google Scholar
[9]Herrmann, R. A., ‘θ-rigidity and the idempotent θ-closure’, Math. Sem. Notes Kobe Univ. 6 (1978), 217–219.Google Scholar
[10]Joseph, J. E., ‘Characterizations of nearly compact spaces’, Boll. Un. Mat. Ital. B (5) 13 (1976), 311–321.Google Scholar
[11]Katětov, M., ‘Über H-abgeschlossene und bikompakte Räume’, Časopis Pěst. Mat. 69 (1940), 36–49.Google Scholar
[12]Mancuso, V. J., ‘Almost locally connected spaces’, J. Austral. Math. Soc. Ser. A 31 (1981), 421–428.Google Scholar
[13]Munshi, B. M. and Bassan, D. S., ‘Super-continuous mappings’, Indian J. Pure Appl. Math. 13 (1982), 229–236.Google Scholar
[14]Nieminen, T., ‘On ultra pseudo compact and related spaces’, Ann. Acad. Sci. Fenn. Ser. A I Math. 3 (1977), 185–205.Google Scholar
[15]Noiri, T., ‘Remarks on locally nearly compact spaces’, Boll. Un. Mat. Ital. (4) 10 (1974), 36–43.Google Scholar
[16]Noiri, T., ‘A note on locally nearly compact spaces’, Bull. Un. Mat. Ital. 12 (1975), 374–380.Google Scholar
[17]Noiri, T., ‘Completely continuous images of nearly paracompact spaces’, Mat. Vesnik 1 (14)(29) (1977), 59–64.Google Scholar
[18]Noiri, T., ‘On δ-continuous functions’, J. Korean Math. Soc. 16 (1980), 161–166.Google Scholar
[19]Papić, P., ‘Sur les espaces presque réguliers’, Glasnik Mat. 4(24) (1969), 303–307.Google Scholar
[20]Porter, J. and Thomas, J., ‘On H-closed and minimal Hausdorff spaces’, Trans. Amer. Math. Soc. 138 (1969), 159–170.Google Scholar
[21]Singal, M. K. and Aiya, S. P., ‘On nearly paracompact spaces’, Mat. Vesnik 6 (21) (1969), 3–16.Google Scholar
[22]Singal, M. K. and Arya, S. P., ‘On almost regular spaces’, Glasnik Mat. 4(24) (1969), 89–99.Google Scholar
[23]Singal, M. K. and Arya, S. P., ‘Almost normal and almost completely regular spaces’, Glasnik Mat. 5 (25) (1970), 141–152.Google Scholar
[24]Singal, M. K. and Mathur, A., ‘On nearly compact spaces’, Boll. Un. Mat. Ital. (4) 2 (1969), 702–710.Google Scholar
[25]Singal, M. K. and Mathur, A., ‘A note on almost completely regular spaces’, Glasnik Mat. 6 (26) (1971), 345–349.Google Scholar
[26]Singal, M. K. and Singal, A. R., ‘Almost continuous mappings’, Yokohama Math. J. 16 (1968), 63–73.Google Scholar
[27]Steen, L. A. and Seebach, J. A., Counterexamples in topology (Holt, Rinehart and Winston, New York, 1970).Google Scholar
[28]Thompson, T., ‘Characterizations of nearly compact spaces’, Kyungpook Math. J. 17 (1977), 37–41.Google Scholar
[29]Veliˇko, N. V., ‘H-closed topological space’, Mat. Sb. 70(112) (1966), 98–21 (Math. USSR-Sb. (2) 78 (1969), 103–118).Google Scholar