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Bounding boxes for compact sets inE 2
 Journal of Formalized Mathematics
, 1997
"... Summary. We define pseudocompact topological spaces and prove that every compact space is pseudocompact. We also solve an exercise from [14] p.225 that for a topological space X the following are equivalent: • Every continuous real map from X is bounded (i.e. X is pseudocompact). • Every continuous ..."
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Summary. We define pseudocompact topological spaces and prove that every compact space is pseudocompact. We also solve an exercise from [14] p.225 that for a topological space X the following are equivalent: • Every continuous real map from X is bounded (i.e. X is pseudocompact). • Every continuous real map from X attains minimum. • Every continuous real map from X attains maximum. Finally, for a compact set in E 2 we define its bounding rectangle and introduce a collection of notions associated with the box.
Bounding Boxes for Compact Sets in Ε²
, 1997
"... this paper. 1. Preliminaries Let X be a set. Let us observe that X has non empty elements if and only if: (Def. 1) 0 / # X. We introduce X is without zero as a synonym of X has non empty elements. We introduce X has zero as an antonym of X has non empty elements. Let us note that R has zero and ..."
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this paper. 1. Preliminaries Let X be a set. Let us observe that X has non empty elements if and only if: (Def. 1) 0 / # X. We introduce X is without zero as a synonym of X has non empty elements. We introduce X has zero as an antonym of X has non empty elements. Let us note that R has zero and N has zero. Let us note that there exists a set which is non empty and without zero and there exists a set which is non empty and has zero. Let us observe that there exists a subset of R which is non empty and without zero and there exists a subset of R which is non empty and has zero. The following proposition is true (1) For every set F such that F is non empty and #linear and has non empty elements holds F is centered. Let