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Question about a Regular Hausdorff Space

Mesfer Alqahtan

New member
Feb 28, 2013
3
If X is T3 space and A infinite subset of X, then the sequence U1, U2,... subset of open set in X,then cl(Un) intersect cl(Um) equal phi for each m not equal n and Un intersect A equal phi.

Prove: since X is T3 then X is regular and T1 then let A be the clouser family of open set in X and B open set subset of A , let U1,u2,... Be subset of B the U1=cl(U1), U2=cl(U2),... (because B is T1) and U1,U2, ... are sigleton then cl(Un) intersect cl(Um) equal phi for each m not equal n and Un intersect A equal phi.
My prove is correct or incorrect