S.O.S. Mathematics CyberBoard

[howi]

A space is called second countable if it has a countable open base. For example, the real line is scond countable because the open intervals where and are rational is a countable open base, since every open interval and hence every open set can be made from unions of these. Show a second countable space is compact if and only if every countable open cover has a finite subcover.

[commutative]

this is an immediate result of Lindelöf theorem, which is quite straightforward:
see it in here: http://planetmath.org/?op=getobj&from=objects&id=3299 [/b]