The following statements about a topological sapce are equivalent: (a) X is a Hausdorff space; (b) The diagonal D = {(x,x): x = X) is closed in XX X.
The following statements about a topological sapce are equivalent: (a) X is a Hausdorff space; (b) The diagonal D = {(x,x): x = X) is closed in XX X.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please do it in simple words and do these proves with full explanation
Transcribed Image Text:The following statements about a topological sapce
are
equivalent:
(a) X is a Hausdorff space;
(b) The diagonal D =
{(x, x): x e X} is closed in X x X.
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