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Algebraic and geometric topology by Symposium in Pure Mathematics Stanford University 1976,

By Symposium in Pure Mathematics Stanford University 1976, Visit Amazon's R. James Milgram Page, search results, Learn about Author Central, R. James Milgram, , American Mathematical Society

Comprises sections on Algebraic $K$- and $L$-theory, surgical procedure and its purposes, team activities

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If Ε i s any e n t o u r a g e The uniform topology of Y then D = (φ^φ) ^E i s an e n t o u r a g e o f X such that false, as φΟ[Η] c Ε[φΗ] Therefore φΗ c φΗ, However, as t h e c o n v e r s e of every undergraduate X = Y =JR, required. student the r e a l f u n c t i o n g i v e n by line, φ(t) uniformly continuous, Similarly for therefore, functions. Under t h e topological equivalences. 11). Let D[xJ φ '•R i s uniformly that φ(x) Let R . i s defined from continuous and continuous equivalences become uniform t o t h e c a t e g o r y of topolog- a s shown by φ : X Y be u n i f o n n l y Then where for Κ c γ φ and each entourage open t h e r e e x i s t s and s o I χ Μ frcra t h e c a t e g o r y of spaces.

E. terminates. of X are the indices of t with each such , with i^ i for < i2 those We t as which . i^^ , then E. = D. t i η l «D. »D. 1, 1 E^ = ΔΧ , if s,t ε I' the diagonal. with s < t then E^ c e ^ . The uniform topology This is o b v i o u s when (k+l)/2n , a r e of case now f o l l o w s t h e form for We now d e f i n e = infit X , ς i EgCxJ remains In f a c t , ζ < s α is α(ξ) if CK/2" , a few s l i p s [10]. in s t The g e n e r a l . index i numerator in a^ . Κ by If ζ ε Η α(ς) = l then .

Zorn's by D - s m a l l Cauchy. 10). 11). only is it as sequentially that each complete, rather d i f f e r e n t sequentially to the sequence. reasons. elementary For m e t r i c spaces space that whereas complete the property X is canplete the r e a l line IR t h e open i n t e r v a l and s o n o t c c m p l e t e . of if (and ccmplete. exeimple, in the Euclidean metric, fore, for are always s p a c e s are a l s o The m e t r i c for if in sequentially T h i s shows, not i s complete s i n c e we c a n a p p l y t h e c o n d i t i o n associated if) X spaces spaces, Obviously c o n p l e t e uniform canplete, space convergent.

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