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Page 56
... homeomorphism in 9 , TM contains a non - void open set V. Thus , TG TM —TMQTM - TM≥ V – V . Since a map of the form y → a ― y is a homeomorphism , the set a - V open . Since the set V - V = ( a - V ) is the union of open sets , it is ...
... homeomorphism in 9 , TM contains a non - void open set V. Thus , TG TM —TMQTM - TM≥ V – V . Since a map of the form y → a ― y is a homeomorphism , the set a - V open . Since the set V - V = ( a - V ) is the union of open sets , it is ...
Page 91
... homeomorphic to a normed linear space if and only if there exists a bounded convex neighborhood of the origin ... homeomorphism between each of the spaces Lp , lp , p≥ 1 , c , co , C [ 0 , 1 ] and the direct sum of these spaces ...
... homeomorphic to a normed linear space if and only if there exists a bounded convex neighborhood of the origin ... homeomorphism between each of the spaces Lp , lp , p≥ 1 , c , co , C [ 0 , 1 ] and the direct sum of these spaces ...
Page 442
... homeomorphism . Q.E.D. Q 8 THEOREM . ( Banach - Stone ) Let Q and R be compact Hausdorff spaces , and let T be an isometric isomorphism between C ( Q ) and C ( R ) . Then there exists a homeomorphism τ between R and Q , and a function a ...
... homeomorphism . Q.E.D. Q 8 THEOREM . ( Banach - Stone ) Let Q and R be compact Hausdorff spaces , and let T be an isometric isomorphism between C ( Q ) and C ( R ) . Then there exists a homeomorphism τ between R and Q , and a function a ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
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A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ