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On some properties of Alexandroff space
Department of Mathematics, Government Engineering College Idukki, Kerala, India.
Review
International Journal of Science and Research Archive, 2024, 13(02), 2563–2569.
Article DOI: 10.30574/ijsra.2024.13.2.2427
Publication history:
Received on 30October 2024; revised on 09 December 2024; accepted on 11 December 2024
Abstract:
The generalized definition of topology is based on the properties of standard Euclidean topology. The goal of this paper is to study spaces that have topologies, which satisfies the stronger condition namely arbitrary intersection of open sets are open. The topological space with this strong property is known as Alexandroff space. With this restriction we lose some important spaces such as Euclidean spaces, but the specialized spaces in turn display interesting properties that are not necessary for a standard Euclidean topology.
Keywords:
Alexandroff space; Euclidean Topolgy; Basis; Posets; Combinatorial topology
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