WebNow an open set is, by definition, a neighbourhood of each of its elements. In the case of a metric space, $\varepsilon$-neighbourhoods can be used, and depending on your definitions and what has already been proved, you may need to use the triangle inequality to …

WebThe definition that you shared from the Wikipedia article defines a limit point in the most abstract (generalized) way, which is important; but this isn't the best definition for building an initial understanding.. In most cases, there exists a distance that allows us to say how far points are from each other (we say that the space is metric).For instance on $\mathbb …