1. Let (X,d) be a metric space. Show that every open d-ball is a d-open subset...

1. Let (X,d) be a metric space.

Show that every open d-ball is a d-open subset of X
Show that every closed d-ball is a d-closed subset of X.

2: Let (X,d) be a metric space. Show that a subset A of X is d-open if and only if it is the union of a (possibly empty) set of open d-balls.

Expert Solution

Here we shall use general definitions of limit point , open set , neighbourhood,open ball , closed set in metric space to prove this question.

Colby Messinger answered 6 months ago

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