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Showing 1 to 2 of 2 for “"Well-Ordering Theorem"”.
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A Proof That Every Set Can be Well-Ordered.
The purpose of this paper is to show that the Well-Ordering Theorem is a consequence of the Axiom of Choice via the Moore-Zermelo Proposition. The work herein is completely my own and is not the result of suggestions made by any other person.
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Concerning the Covering Theorem for Closed and Perfectly Compact Point Sets.
… a consequence of R. L. Moore’s Axiom 0 and the Well-Ordering Theorem, 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.