SOLVE STEP BY STEP IN DIGITAL FORMATヅツッシÜ♡* * ??!!??! ¿¡ !?! XX X X X XO3*✓✓7. Let (X, T)Jbe a topological space and x € X. We say that Bx is a "local basis" for x if given U E T,there exists B EB such that x E B C U.On the other hand, a (X, T)countability) if every point in the space has a local countable basis.Show that the property of being 1st countable is a topological property.space is said to be 1-countable (1st countable or satisfies the first axiom of

Given: 7. A topological space X, τ is said to be first countable if it has countable local basis at…

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.