Question: Prove the question without using the dense and separable properties Prove that if a topological space (X,) has an uncountable isolated points, then it cannot

Prove the question without using the dense and separable properties

Prove that if a topological space (X,) has an uncountable isolated points, then it cannot be second countable. Hint: If x is an isolated point in X, must {x} be in any base for (X,)

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