Sheff Posted October 14, 2016 Share Posted October 14, 2016 Let's call a set "Pseudo compact" if it has the property that every closed cover (a cover consisting of closed sets) have a finite subcover. Does "Pseudo Compact" in this case the same as "Anti-Compact" ? Then how can we describe the "Pseudo-Compact" subsets of Real Numbers? Link to comment Share on other sites More sharing options...
Country Boy Posted October 14, 2016 Share Posted October 14, 2016 Thank you for giving the definition of "pseudo-compact". Now, it would help if you would give the definition of "anti-compact'! Link to comment Share on other sites More sharing options...
Country Boy Posted October 16, 2016 Share Posted October 16, 2016 Thank you for giving the definition of "pseudo-compact". Now, it would help if you would give the definition of "anti-compact'! Added: I have found two definitions of "anti-compact": 1) a subset A in a topological space X is anti-compact if every covering of A by closed sets has a finite subcover. 2) anti-compact means that the only compact subsets of X are the finite ones. Link to comment Share on other sites More sharing options...
blue89 Posted November 2, 2016 Share Posted November 2, 2016 there ,I see something like equivalency between two part of analysis. if all sequences have convergent subsequences at any (X) set X is said to be compact. (f.analysis) The descriptions in real analysis seem like another descriptions. basic and or functional analysis. of course topology might contain more different ones. Link to comment Share on other sites More sharing options...
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