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(Solved):   H.w Prove that \( B_{\varepsilon}(A) \in \tau d \) for all \( A \subseteq x \) and \( \var ...


H.w Prove that \( B_{\varepsilon}(A) \in \tau d \) for all \( A \subseteq x \) and \( \varepsilon>0 \) and \( A \subseteq B_{

 

H.w Prove that \( B_{\varepsilon}(A) \in \tau d \) for all \( A \subseteq x \) and \( \varepsilon>0 \) and \( A \subseteq B_{\varepsilon}(A) \)


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Step 1: Let A?X be a subset of a topological space X with a topology ?d. Step 2: For any ? > 0, define B_? (A) as the ?-neighborhood of A, that is, B_
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