Bounding Boxes for Compact Sets in E
نویسندگان
چکیده
We define pseudocompact topological spaces and prove that every compact space is pseudocompact. We also solve an exercise from [16] p.225 that the 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 we define its bounding rectangle and introduce a collection of notions associated with the box.
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