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?

Thank you for giving the definition of "pseudo-compact". Now, it would help if you would give the definition of "anti-compact'!

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.

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.