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APPLICATIONS TO MATHEMATICAL ANALYSIS AND TOPOLOGY
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assume axiom is satisfied b e P(t B-space bijection Chapter compact space concrete control system contradiction Corollary corresponding p-topology countably compact D.P.P. which satisfies define dynamic programming problems elements Example exists x e F is p-bijective finite following axiom following properties induced inf B2 interval topology isomorphic knapsack problem Lemma let F Let P,T Let u,v e Let x e Let x,y e max(P,U metric space Notation open covering operations research optimal policy optimization problems optimizing sequence p-connected p-injective P,f_ preordered set Proof properties are equivalent pt|t e relative topology result follows result is proven satisfies D.P.2 satisfies O.C.2(b satisfies O.C.6 second countable sequential S.D.P.P. sets D(x subproblem subsets sup Bj Suppose Theorem tj,b topological space total order totally ordered set totally preordered u,v e x e g(u x e P(a x(tQ y e g(v