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... U i and if X is normal, then open Vi such that with Fi ____ Fi Vi Vi U i . This is the argument of the case k=2. Then by induction we can prove the statement. Suppose we proved X normal for any open____cover {U1 ,,U k } open shrinking ' {V1,,V2}, ' is a cover and Vi U i . ...
... U i and if X is normal, then open Vi such that with Fi ____ Fi Vi Vi U i . This is the argument of the case k=2. Then by induction we can prove the statement. Suppose we proved X normal for any open____cover {U1 ,,U k } open shrinking ' {V1,,V2}, ' is a cover and Vi U i . ...
Natural covers
... each topological space X a cover 1 x satisfying 1) if S E 03A3X and S is homeomorphic to a subset T of Y, then T ~03A3Y, and 2 ) if f : X - Y is continuous and S e27y there is a T e27y with f(S) C T. For example we may chooseex to be the compact subsets of X, or the connected subsets, or the countab ...
... each topological space X a cover 1 x satisfying 1) if S E 03A3X and S is homeomorphic to a subset T of Y, then T ~03A3Y, and 2 ) if f : X - Y is continuous and S e27y there is a T e27y with f(S) C T. For example we may chooseex to be the compact subsets of X, or the connected subsets, or the countab ...
Second category incomplete normed spaces Let us recall that a
... Second category incomplete normed spaces Let us recall that a nowhere dense set in a topological space is a set which is not dense in any nonempty open set. Countable unions of nowhere dense sets are called first category sets (or sets of first [Baire] category). Sets which are not of the first cate ...
... Second category incomplete normed spaces Let us recall that a nowhere dense set in a topological space is a set which is not dense in any nonempty open set. Countable unions of nowhere dense sets are called first category sets (or sets of first [Baire] category). Sets which are not of the first cate ...
