• Title/Summary/Keyword: minimal open sets and maximal open sets

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ON SOME NEW MAXIMAL AND MINIMAL SETS VIA θ-OPEN SETS

  • Caldas, Miguel;Jafari, Saeid;Moshokoa, Seithuti P.
    • Communications of the Korean Mathematical Society
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    • v.25 no.4
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    • pp.623-628
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    • 2010
  • Nakaoka and Oda ([1] and [2]) introduced the notion of maximal open sets and minimal closed sets in topological spaces. In this paper, we introduce new classes of sets called maximal $\theta$-open sets, minimal $\theta$-closed sets, $\theta$-semi maximal open and $\theta$-semi minimal closed and investigate some of their fundamental properties.

ON MAXIMAL, MINIMAL OPEN AND CLOSED SETS

  • MUKHARJEE, AJOY
    • Communications of the Korean Mathematical Society
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    • v.30 no.3
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    • pp.277-282
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    • 2015
  • We obtain some conditions for disconnectedness of a topological space in terms of maximal and minimal open sets, and some similar results in terms of maximal and minimal closed sets along with interrelations between them. In particular, we show that if a space has a set which is both maximal and minimal open, then either this set is the only nontrivial open set in the space or the space is disconnected. We also obtain a result concerning a minimal open set on a subspace.

ON FUZZY MAXIMAL, MINIMAL AND MEAN OPEN SETS

  • SWAMINATHAN, A.;SIVARAJA, S.
    • Journal of Applied and Pure Mathematics
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    • v.4 no.1_2
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    • pp.79-84
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    • 2022
  • We have observed that there exist certain fuzzy topological spaces with no fuzzy minimal open sets. This observation motivates us to investigate fuzzy topological spaces with neither fuzzy minimal open sets nor fuzzy maximal open sets. We have observed if such fuzzy topological spaces exist and if it is connected are not fuzzy cut-point spaces. We also study and characterize certain properties of fuzzy mean open sets in fuzzy T1-connected fuzzy topological spaces.

MORE ON FUZZY MAXIMAL, MINIMAL OPEN AND CLOSED SETS

  • SWAMINATHAN, A.;SIVARAJA, S.
    • Journal of applied mathematics & informatics
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    • v.39 no.3_4
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    • pp.251-257
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    • 2021
  • This article is devoted to introduce the notion of fuzzy cleanly covered fuzzy topological spaces; in addition two strong fuzzy separation axioms are studied. By means of fuzzy maximal open sets some properties of fuzzy cleanly covered fuzzy topological spaces are obtained and also by means of fuzzy maximal closed sets few identical results of a fuzzy topological spaces are investigated. Through fuzzy minimal open and fuzzy maximal closed sets, two strong fuzzy separation axioms are discussed.

MORE ON MAXIMAL, MINIMAL OPEN AND CLOSED SETS

  • Mukharjee, Ajoy
    • Communications of the Korean Mathematical Society
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    • v.32 no.1
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    • pp.175-181
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    • 2017
  • In this paper, we introduce a notion of cleanly covered topological spaces along with two strong separation axioms. Some properties of cleanly covered topological spaces are obtained in term of maximal open sets including some similar properties of a topological space in term of maximal closed sets. Two strong separation axioms are also investigated in terms of minimal open and maximal closed sets.

SOME EXTENSION ON HESITANT FUZZY MAXIMAL, MINIMAL OPEN AND CLOSED SETS

  • M. SANKARI;C. MURUGESAN
    • Journal of applied mathematics & informatics
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    • v.41 no.2
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    • pp.265-272
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    • 2023
  • This article presents a novel notion of hesitant fuzzy cleanly covered in hesitant fuzzy topological spaces;moreover two strong hesitant fuzzy separation axioms are investigated. Based on fuzzy maximal open sets few properties of hesitant fuzzy cleanly covered are obtained. By dint of hesitant fuzzy minimal open and fuzzy maximal closed sets two strong hesitant fuzzy separation axioms are extended.

On Mean Open and Closed Sets

  • Mukharjee, Ajoy;Bagchi, Kallol Bhandhu
    • Kyungpook Mathematical Journal
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    • v.56 no.4
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    • pp.1259-1265
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    • 2016
  • In this paper, we introduce the notions of mean open and closed sets in topological spaces, and obtain some properties of such sets. We observe that proper paraopen and paraclosed sets are identical to mean open and closed sets respectively.

On Paraopen Sets and Maps in Topological Spaces

  • Ittanagi, Basavaraj M.;Benchalli, Shivanagappa S.
    • Kyungpook Mathematical Journal
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    • v.56 no.1
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    • pp.301-310
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    • 2016
  • In this paper, we introduce and study the concept of a new class of sets called paraopen sets and paraclosed sets in topological spaces. During this process some of their properties are obtained. Also we introduce and investigate a new class of maps called paracontinuous, *-paracontinuous, parairresolute, minimal paracontinuous and maximal paracontinuous maps and study their basic properties in topological spaces.

FUZZY COMPACTNESS, FUZZY REGULARITY VIA FUZZY MAXIMAL OPEN AND FUZZY MINIMAL CLOSED SETS

  • SWAMINATHAN, A.;SIVARAJA, S.
    • Journal of applied mathematics & informatics
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    • v.40 no.1_2
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    • pp.185-190
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    • 2022
  • The aim of this article is to define fuzzy maximal open cover and discuss its few properties. we also defined and study fuzzy m-compact space and discussed its properties. Also we obtain few more results on fuzzy minimal c-regular and fuzzy minimal c-normal spaces. We have proved that a fuzzy Haussdorff m-compact space is fuzzy minimal c-normal.