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Showing 1 to 3 of 3 for “"Compact point sets"”.
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Concerning the Covering of Closed and Compact Point Sets.
… basic definitions to prove that every closed and compact point set which is covered by a collection of domains is covered by a finite subcollection of those domains.
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A Covering Theorem for Closed and Compact Point Sets.
… Axiom 0 and Axiom 13 that if M is a closed and compact point set and Gis a collection of domains covering M, then there is a finite subcollection of G which covers M. All of the work presented in this thesis, including the proofs of all of the theorems, is my own.
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Concerning the Covering Theorem for Closed and Perfectly Compact Point Sets.
… the following is a theorem: If M is a closed point set, then M is perfectly compact if, and only if, when G is a collection of regions covering M, then some finite subcollection of G covers M.