Abstract
We define and study complete generalized neighborhood systems, and prove that a generalized neighborhood system is complete if and only if it can be generated by a generalized topology. Also we obtain some applications of complete generalized neighborhood systems.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Á. Császár, Generalized open sets, Acta Math. Hungar., 75 (1997), 65–87.
Á. Császár, Generalized topology, generalized continuity, Acta Math. Hungar., 96 (2002), 351–357.
Á. Császár, Generalized open sets in generalized topologies, Acta Math. Hungar., 106 (2005), 53–66.
Á. Császár, On generalized neighborhood systems, Acta Math. Hungar., 121 (2008), 395–400.
W. K. Min, Generalized topological spaces and generalized systems, Acta Math. Hungar., 108 (2005), 171–181.
W. K. Min, On weak neighborhood systems and spaces, Acta Math. Hungar., 121 (2008), 283–292.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by China Postdoctoral Science Foundation funded project(No.20090461093), Jiangsu Planned Projects for Postdoctoral Research Funds (No. 0902064C) and NSFC (No. 10971185).
Rights and permissions
About this article
Cite this article
Shen, R. Complete generalized neighborhood systems. Acta Math Hung 129, 160–165 (2010). https://doi.org/10.1007/s10474-010-9258-8
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10474-010-9258-8
Key words and phrases
- generalized neighborhood system
- generalized topology
- generalized interior operator
- complete generalized neighborhood system