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Suppose that X is a non-empty, complete, and countable metric space. Use Baire Category Theorem only...

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Advance Math

Suppose that X is a non-empty, complete, and countable metricspace. Use Baire Category Theorem only to prove directly that X hasan isolated point. Include a precise statement of the theorem inyour proof and indicate how it is being applied.

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Let d be metric defined on the non empty set X which iscountable and the metric space is completeWant to prove that X has an isolatedpointWe will prove it by the method of contradictionNow suppose X doesnt    See Answer
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