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Page 14
Q.E.D. 17 Lemma. // X, Y, Z are topological spaces, and if f : X Y and g : Y -> Z arc
continuous, then the composite function fg is continuous. The term scalar will be
used for a real or complex number; a scalar function is a real or complex valued ...
Q.E.D. 17 Lemma. // X, Y, Z are topological spaces, and if f : X Y and g : Y -> Z arc
continuous, then the composite function fg is continuous. The term scalar will be
used for a real or complex number; a scalar function is a real or complex valued ...
Page 381
10], Hewitt [3] and Edwards [1] consider functionals on the space of continuous
functions on a locally compact Hausdorff space which vanish outside of compact
sets. Arens [3] discussed certain sub-algebras of continuous functions on a ...
10], Hewitt [3] and Edwards [1] consider functionals on the space of continuous
functions on a locally compact Hausdorff space which vanish outside of compact
sets. Arens [3] discussed certain sub-algebras of continuous functions on a ...
Page 841
criteria for the limit to be continuous, 1.7.7 (29), IV.6.11 (268) definition, 1.4.15 (13
) density in TM and L„, III.9.14 (170), IV.8.19 (298) existence of non-differentiable
continuous functions, 1.9.6 (33) existence on a normal space, 1.5.2 (15) ...
criteria for the limit to be continuous, 1.7.7 (29), IV.6.11 (268) definition, 1.4.15 (13
) density in TM and L„, III.9.14 (170), IV.8.19 (298) existence of non-differentiable
continuous functions, 1.9.6 (33) existence on a normal space, 1.5.2 (15) ...
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
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a-field Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact operator complex numbers complex valued contains continuous functions continuous linear convex set Corollary countably additive Definition denote dense differential equations disjoint sets Doklady Akad Duke Math element equivalent everywhere exists extended real valued extension finite dimensional finite number function f Hausdorff space Hence Hilbert space homeomorphism inequality interval Lebesgue measure lim sup linear functional linear map linear operator linear topological space LP(S measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space null set open set operator topology positive measure space Proc Proof properties proved real numbers Riesz Russian semi-group sequentially compact Show simple functions subset subspace Suppose theory topological space Trans uniformly unique v(fi valued function Vber vector valued weakly compact