Handbook of Analysis and Its Foundations
Academic Press, 24 okt. 1996 - 883 pagina's
Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook.
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assume Axiom of Choice Banach space Boolean algebra bounded Cauchy Chapter cl(S closed closure collection compact contains continuous functions convergence countable Dedekind complete defined definition denoted disjoint dual Eacamples element equation equicontinuous equipped examples exists F-seminorm finite set follows formula function f gauge given Hausdorff hence Hint homomorphism infinite instance integral isomorphism lattice lattice group Lemma Let f Let Q linear map linear space linear subspace locally convex logic mapping f mathematicians mathematics measure space metric space morphism neighborhood nonempty normed space notation o-algebra open set operations ordered pointwise positive integer product topology Proof prove pseudometric pseudometric space quotient real numbers Remarks result satisfies scalar field seminorm sequence set theory subset suffices to show Suppose symbols syntactic theorem topological space topological vector space ultrafilter uniform space uniformly variables