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Page 21
... dense in a topological space X , if its closure is X. It is said to be nowhere dense if its closure does not contain any open set . A space is separable , if it contains a denumer- able dense set . 12 THEOREM . If a topological space ...
... dense in a topological space X , if its closure is X. It is said to be nowhere dense if its closure does not contain any open set . A space is separable , if it contains a denumer- able dense set . 12 THEOREM . If a topological space ...
Page 450
... dense subset of its boundary . PROOF . Let K be the convex set . It will be shown that -7 ( x , y ) · T ( x , y ) , y € X , for x in a dense subset Z of X. The set K contains some sphere S ( 0 , 1 / N ) about the origin . This clearly ...
... dense subset of its boundary . PROOF . Let K be the convex set . It will be shown that -7 ( x , y ) · T ( x , y ) , y € X , for x in a dense subset Z of X. The set K contains some sphere S ( 0 , 1 / N ) about the origin . This clearly ...
Page 842
... Dense convex sets , V.7.27 ( 437 ) Dense linear manifolds , V.7.40-41 ( 438-439 ) Dense set , definition , I.6.11 ( 21 ) density of simple functions in L , 1 ≤ p < ∞ , III.3.8 ( 125 ) density of continuous functions in TM and L , III ...
... Dense convex sets , V.7.27 ( 437 ) Dense linear manifolds , V.7.40-41 ( 438-439 ) Dense set , definition , I.6.11 ( 21 ) density of simple functions in L , 1 ≤ p < ∞ , III.3.8 ( 125 ) density of continuous functions in TM and L , III ...
Contents
B Topological Preliminaries | 10 |
Metric Spaces | 23 |
Product Spaces | 31 |
Copyright | |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ ba(S Banach spaces Borel sets Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations Doklady Akad Duke Math E₁ elements ergodic exists extension f₁ function defined function f Hausdorff space Hence Hilbert space homomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz Russian S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-integrable u-measurable u-null uniformly unit sphere valued function vector space weakly compact zero ΕΕΣ