Solution Of Topology

topology generated by arithmetic progression basis is Hausdor . Hint. If m 1 >m 2 then consider open sets fm 1 + (n 1)(m 1 + m 2 + 1)g and fm 2 + (n 1)(m 1 + m 2 + 1)g. The following observation justi es the terminology basis: Proposition 4.6. If B is a basis for a topology on X;then B is the col-lection TOPOLOGY: NOTES AND PROBLEMS Page 2/3 ................
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