Hostname: page-component-7479d7b7d-qlrfm Total loading time: 0 Render date: 2024-07-13T12:30:37.701Z Has data issue: false hasContentIssue false
  • English
  • Français

CONTINUITY ON GENERALISED TOPOLOGICAL SPACES VIA HEREDITARY CLASSES

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

Published online by Cambridge University Press:  21 February 2018

P. MONTAGANTIRUD Open the ORCID record for P. MONTAGANTIRUD [Opens in a new window]  and
W. THAIKUA
P. MONTAGANTIRUD*
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand email pongdate.m@chula.ac.th
W. THAIKUA
Affiliation:
Department of Mathematics and Computer Science, Faculty of Science, Chulalongkorn University, Bangkok 10330, Thailand email wichitponkids@hotmail.com
*
✉pongdate.m@chula.ac.th
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.

A generalised topology is a collection of subsets of a given nonempty set containing the empty set and arbitrary unions of the elements in the collection. By using the concept of hereditary classes, a generalised topology can be extended to a new one, called a generalised topology via a hereditary class. We study continuity on generalised topological spaces via hereditary classes in various situations.

Keywords

generalised topological spaces(𝜇, 𝜈)-continuous functionshereditary classes

MSC classification

Primary: 54A05: Topological spaces and generalizations (closure spaces, etc.)
Secondary: 54C05: Continuous maps 54C08: Weak and generalized continuity
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 97 , Issue 2 , April 2018 , pp. 320 - 330
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

References

Császár, Á., ‘Generalized open sets’, Acta Math. Hungar. 75 (1997), 65–87.Google Scholar
Császár, Á., ‘Generalized topology, generalized continuity’, Acta Math. Hungar. 96 (2002), 351–357.Google Scholar
Császár, Á., ‘Generalized open sets in generalized topologies’, Acta Math. Hungar. 108 (2005), 53–66.Google Scholar
Császár, Á., ‘Modification of generalized topologies via hereditary classes’, Acta Math. Hungar. 115 (2007), 29–36.Google Scholar
Hamlett, T. R. and Janković, D., ‘New topologies from old via ideals’, Amer. Math. Monthly 97 (1990), 295–310.Google Scholar
Renukadevi, V. and Vimladevi, P., ‘Compatible hereditary classes in GTS’, Acta Math. Hungar. 147 (2015), 259–271.Google Scholar