1) B={(a,b)|a,b are rational numbers} is a countable base for the usual topology for the real numbers.

2) For any topologies T1 and T2 for X, if B1 is a base for T1 and B1 is a subset of T1, then T1 is a subset of T2

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- Sep 24th 2012, 11:28 AMKieferTopology Proofs, Bases
1) B={(a,b)|a,b are rational numbers} is a countable base for the usual topology for the real numbers.

2) For any topologies T1 and T2 for X, if B1 is a base for T1 and B1 is a subset of T1, then T1 is a subset of T2 - Sep 24th 2012, 11:56 AMgirdavRe: Topology Proofs, Bases
Where are you stuck? Is it clear that B is countable in the first question?