More on maximal, minimal open and closed sets
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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.
Abstract
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.
참고문헌 (6)
- P. Howard, "On the minimal cover property in ZF", Topology Appl, 173, pp.94~106 (2014)
- Ajoy Mukharjee, "On maximal, minimal open and closed sets", 대한수학회논문집, 30(3), pp.277~282 (2015), 대한수학회
- F. Nakaoka, "Some applications of minimal open sets", Int. J. Math. Math. Sci, 27(8), pp.471~476 (2001)
- F. Nakaoka, "Some properties of maximal open sets", Int. J. Math. Math. Sci, 21(21), pp.1331~1340 (2003)
- F. Nakaoka, "Minimal closed sets and maximal closed sets", Int. J. Math. Math. Sci, 2006, pp.8~ (2006)
- L. A. Steen, "Counterexamples in topology" (1970), Holt, Rinehart and Winston Inc.