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A Note on Kuratowski’s Theorem and Its Related Topics

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Document pages: 24 pages

Abstract: In point set topology, it is well known that the Kuratowski 14-set problem isone of the most interesting results. In this note, we first give a brief survey ofthe Kuratowski’s theorem. In particular, we will study and investigate thestructure of the boundary of a given subset in a topological space. Some newresults and topics which are related to the theorem of Kuratowski are presentedand discussed. Finally, we pose some open problems of Kuratowskitype.

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