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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.
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참고문헌 (4)
참고문헌 신청
F. Nakaoka / 2001 / Some applications of minimal open sets / Int. J. Math. Math. Sci 27 (8) : 471 ~ 476
F. Nakaoka / 2003 / Some properties of maximal open sets / Int. J. Math. Math. Sci 2003 (21) : 1331 ~ 1340
F. Nakaoka / 2006 / Minimal closed sets and maximal closed sets / Int. J. Math. Math. Sci : 1 ~ 8
S. Willard / 1970 / General Topology / Addison-Wesley Publishing Company
F. Nakaoka / 2003 / Some properties of maximal open sets / Int. J. Math. Math. Sci 2003 (21) : 1331 ~ 1340
F. Nakaoka / 2006 / Minimal closed sets and maximal closed sets / Int. J. Math. Math. Sci : 1 ~ 8
S. Willard / 1970 / General Topology / Addison-Wesley Publishing Company
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