We say a point x in X (which is a topological space) is an accumulation point of A if and only if any open set containing x has a non-empty intersection with A-{x}.(adsbygoogle = window.adsbygoogle || []).push({});

Well, I'm creating examples for myself to understand the definition.

Suppose X={a,b,c,d,e} and define T={∅,{a,b},{b,c,d},{a,b,c,d},X}. T is a topology on X. Now I'm trying to find the set of all accumulation points of {b,c,d}.

a,c and d are accumulation points of {b,c,d}, b is not an accumulation point of it, but I'm not sure if I should consider e an accumulation point of {b,c,d} or not because there is no open set containing e in my topology defined on X. Should I consider e an accumulation point because the antecedent in the definition (where it assumes that there exists an open set containing that point) is false for e?

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# Accumulation point definition.

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