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Indeed I am quite confused with the definition of neighborhood of a point x since I come across two versios of it.

The first one is simply defined as open set of x while the second one is defined as a set containing an open set of x.

Apparently these two are different notions, e.g. (x-a, x+a], in first one this is not a neighborhood while the second one it is.

So which one is the right one? Thanks very much.

Wayne

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# Definition of neighborhood

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