Question: Please help with this. Let A be a set in a metric space ( X , ? ) . Show that, for each open set

Please help with this.

Let A be a set in a metric space (X,?).

Show that, for each open set O in (X,?),

O?A?=??O?A?=?.

REFERENCES

Please help with this. Let A be a set in a metric

Theorem 2.13 {Characterizations of Closed Sets]. Let (X, p} be a metric space and A g X. Then the fattening statements are equivalent: 1. A is closed in (Jinn). 2. The complement Ac is open. 3. (Sequential Characterization) For any sequence {xl E A convergent in (X,p), limnqm x" e A, i. e., A contains the limits ofatt its convergent sequences. Theorem 2.1:: [SequentialCharacterizations of Open Sets}. Let ip) be e metric space. A set A E X is open in [X,p) W, for any sequence {x'l ; X convergent In a paint x e A, {xl is eventually in A

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