대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제38권1호
  • /
  • Pages.267-280
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  • 2023
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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ON COVERING AND QUOTIENT MAPS FOR 𝓘𝒦-CONVERGENCE IN TOPOLOGICAL SPACES

  • Debajit Hazarika (Department of Mathematical Sciences Tezpur University) ;
  • Ankur Sharmah (Department of Mathematical Sciences Tezpur University)
  • 투고 : 2022.02.05
  • 심사 : 2022.05.16
  • 발행 : 2023.01.31
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초록

In this article, we show that the family of all 𝓘𝒦-open subsets in a topological space forms a topology if 𝒦 is a maximal ideal. We introduce the notion of 𝓘𝒦-covering map and investigate some basic properties. The notion of quotient map is studied in the context of 𝓘𝒦-convergence and the relationship between 𝓘𝒦-continuity and 𝓘𝒦-quotient map is established. We show that for a maximal ideal 𝒦, the properties of continuity and preserving 𝓘𝒦-convergence of a function defined on X coincide if and only if X is an 𝓘𝒦-sequential space.

키워드

과제정보

The first author would like to thank the University Grants Comission (UGC) for awarding the junior research fellowship vide UGC-Ref. No.: 1115/(CSIR-UGC NET DEC. 2017), India.

참고문헌

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