On the functionally countable subalgebra of C(X)
We prove that a Hausdorff space is locally compact if and only if its topology coincides with the weak topology induced by . It is shown that for a Hausdorff space , there exists a locally compact Hausdorff space such that . It is also shown that for locally compact spaces and , if and only if . Prime ideals in are uniquely represented by a class of prime ideals in . -compact spaces are introduced and it turns out that a locally compact space is -compact if and only if every...
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