Show that a metric space X is not connected if and only if there exists a...

Question

Question

Show that a metric space X is not connected if and only if there exists a continuous surjection f : X → {0, 1}.

math Advanced-Math

Answer 1

Answer #1

Let X is disconnected. Then there exists open Sets A,8 CX Such thal X AUB and AnB degfine txoy Let us txEB Ther f Pastng is c

Answer 2

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