# Is R Compact with This Topology?

Please solve the following problem:

" Let X be any set with infinite elements ; is it true that

A = { A a subset of X : X - A is either finite or countable} U { X,0} is a topology on X ?. Why ? ( note: the 0 means the empty set).

Is R compact with this topology?

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#### Solution Summary

The solution determines if R is compact with the topology.

$2.19