Tony Bryant, Veena Syan's Adopting the Process View: A Case Study of Modeling Change PDF

By Tony Bryant, Veena Syan

ISBN-10: 0585432864

ISBN-13: 9780585432861

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Additional resources for Adopting the Process View: A Case Study of Modeling Change in the Not-for-Profit Sector

Example text

Let cpn : (n = 1,2, . . 1 and let cp : X+Y. X+Y We say that cpn convewes &Q cp c uniformly neighborhood U bf x and an integer No < c d(cp(x'),cpn(x')) for n every c > 0, we say x, for every x E No. E at x if there is a n c such that if x' E U, If cpn-+cp uniformly at x c uniformly at x. Q +cp easy to check that cpn-+cp at 2 X and > 0. Let x If X for is compact, it is uniformly if and only if cpn+cp uniformly X. 12. Lemma. , the countable intersection of open dense sets is dense) and let cpn be a sequence of continuous functions from X x Let E be the set of x X.

Or more precisely the family of self maps of X Proof. We regard T which T defines) as a subset of C(X,X) the continuous maps from X to itself, provided with the topology of uniform convergence. sufficient by the Ascoli-Arzelk theorem, to show that T compact in C(X,X). Let {ti) is relatively be a sequence in T and let x E X. 0 Then there is a subsequence which we still call {ti) such that lim xOti exists. It follows from the transitivity of A exists for every x E X. Then there is a map t i +h (h(x) = lim xt pointwise i lim cp(x)ti = lim cp(xti) = cp(h(x)).

The final result in this chapter gives a sufficient condition for Chapter 2 44 equicontinuity in terms of the action of the automorphism group. The proof depends on a lemma from general topology which is not quite standard, s o we include it here. Let X be a topological space, and let Y be a metric space. Let cpn : (n = 1,2, . . 1 and let cp : X+Y. X+Y We say that cpn convewes &Q cp c uniformly neighborhood U bf x and an integer No < c d(cp(x'),cpn(x')) for n every c > 0, we say x, for every x E No.

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Adopting the Process View: A Case Study of Modeling Change in the Not-for-Profit Sector by Tony Bryant, Veena Syan


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