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New Continuity Concepts With Usual, Semi, and Semi‐ω‐Closure Operators

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  • Kushal Singh
  • Asha Gupta

Abstract

In this paper, we introduce new forms of continuity, namely, weakly θs‐continuity, weakly θsω‐continuity, almost θs‐continuity, and almost θsω‐continuity defined via closure operators. These concepts bridge the gap between classical and weak continuity and provide new insights into their relationships. We establish necessary and sufficient conditions under which these forms align with existing notions such as semi‐θs‐continuity, θsω‐continuity, weak continuity, and usual continuity, especially under specific constraints on the domain or codomain space. Our findings highlight both the common ground and the key differences between weakly and almost continuity concepts. To support and illustrate our findings, the study incorporates a wide range of examples and counterexamples, providing a comprehensive understanding of these concepts.

Suggested Citation

  • Kushal Singh & Asha Gupta, 2025. "New Continuity Concepts With Usual, Semi, and Semi‐ω‐Closure Operators," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jjmath:v:2025:y:2025:i:1:n:8411230
    DOI: 10.1155/jom/8411230
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    References listed on IDEAS

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    1. Krätschmer, Volker & Schied, Alexander & Zähle, Henryk, 2017. "Domains of weak continuity of statistical functionals with a view toward robust statistics," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 1-19.
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