Is this definition of boundary points correct?
The point $x$ is said to be a boundary point or a frontier point of the set $M$ if it is not an interior point either of $M$ or of $M^c$ the complement of $M$.
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1I think the better definition is given here – amWhy Oct 30 '20 at 17:19
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I know about this definition and if you think about it they are the same thing, but I wanted to define boundary points without referring to open balls – Tarek Acila Oct 30 '20 at 17:27
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1Then your task is to demonstrate the two definitions are equivalent, @Tarek. – amWhy Oct 30 '20 at 17:33
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1@TarekAcila - replace "open ball" with "open set", and the definition suddenly applies to any topological space. – Paul Sinclair Oct 31 '20 at 00:57