7. Let (X, T) be a topological space and xe X. We say that Bx CT is a "local basis" for x if given U E T, there exists B E B such that x EBCU. On the other hand, a (X, T) space is said to be 1-countable (1st countable or satisfies the first axiom of countability) if every point in the space has a local countable basis. Show that the property of being 1st countable is a topological property.

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Q: be a n-dimensional normed space, then prove that its dual space is also n-dimensional.

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Q: (c) If X={1, 2, 3}. T= {4, X, {1}, {1,2}, {3}, {1,3}}. JUSTIFY whether the topological space (X, t)…

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