in S which converges to q. Corollary 1 Every point in the boundary of a set S is simultaneously the limit of a convergin

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In S Which Converges To Q Corollary 1 Every Point In The Boundary Of A Set S Is Simultaneously The Limit Of A Convergin 1 (24.8 KiB) Viewed 35 times

in S which converges to q. Corollary 1 Every point in the boundary of a set S is simultaneously the limit of a converging sequence of points in S and a converging sequence of points in the complement of S. For, by item (viii) in the list of basic topological facts (1-29), bdy(S) is the intersection of the closure of S and the closure of the complement of S. Corollary 2 A ser S is closed if and only if it contains the limit of every converging sequence (p) whose terms lie in S.