Are my definitions of interior and closure correct?

[Ricster55]

Homework Statement

Define the interior A◦ and the closure A¯ of a subset of X.
Show that x ∈ A◦ if and only if there exists ε > 0 such that B(x,ε) ⊂ A.

The Attempt at a Solution

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[Stephen Tashi]

It would be best not to use abbreviations like "(+) real #" unless your instructor uses such notation.

How things are defined in a metric space can vary from author to author. The fact that you mention "neighborhood" and "open set" makes me wonder if the definitions of "interior of A" and "closure of A" in your text materials might use those terms.

If those two definitions in you text materials don't mention "neighborhood" and "open set" then I see no need to mention them in this particular problem. Does your text define "interior of A" and "closure of A" only using the concept of an open ball $B(x,\epsilon)$ ?