Hrituraj Pal, Md Mirazul Hoque, Baby Bhattacharya, Jayasree Chakraborty

A study on δ‐ℐ‐compactness in a mixed fuzzy ideal topological space

  • Applied Mathematics
  • Computational Theory and Mathematics
  • Statistics, Probability and Uncertainty
  • Mathematical Physics
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Abstract The role of fuzzy 𝛿-open set is highly significant in the study of fuzzy topology initiated by Ganguly and Saha [S. Ganguly and S. Saha, A note on 𝛿-continuity and 𝛿-connected sets in fuzzy set theory, Simon Stevin 62 (1988), 2, 127–141]. This article begins with the introduction of 𝛿-ℐ-open covers in a mixed fuzzy ideal topological space. After that, we introduce 𝛿-ℐ-compactness and then some properties of its are discussed therein. It is shown that the aforesaid compactness is the weaker form of fuzzy compactness. Moreover, we show that if we retopologize the fuzzy topology then in the new environment fuzzy 𝛿-ℐ-compactness and fuzzy compactness are equivalent. In addition, we introduce two different notions of continuity and investigate the behavior between fuzzy 𝛿-ℐ-compactness and fuzzy compactness.

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