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By Tammo tom Dieck

This publication is a jewel– it explains very important, beneficial and deep issues in Algebraic Topology that you just won`t locate in other places, conscientiously and in detail."""" Prof. Günter M. Ziegler, TU Berlin

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L. Bentley and H. Herrlich [4], and H. L. Bentley [3]. Near denotes the category of nearness spaces, a subcategory of Mer. It contains Top as a bicoreflective subcategory. Also, Near has a pleasant completion operation X + X* which generalizes the completion for uniform spaces. Near also contains (as either bireflective or bicoreflective subcategories) each of the other categories Reg, Normal and Unif mentioned below. Near-1 denotes the category of nearness spaces whose underlying topological space is a Tl-space.

And . If we set h = L 1 1 JE . Moreover, qBo(l 1 ) n+l n~ g R + 1/2 )6N for n > 1 . Thus (1/2 have ~ For in Ebd Bv c Ev, B~ v = 1,2,3,4 = Bv, v = n > 1 , let fv: Ev ~ f' v of fv Ev+l then we be absolutely summing mappings B1 c E 1 , B~ 0 = B1 there exist sets 2, ... S. c(qv)(xi)I (xi)I E l~(Ev) , v = 1, ... ,4 restriction for and is nuclear. between bornological spaces. 6. Theorem. bornological spaces Proof: n s (1 + (1/4)6) (qv denotes the gauge function for (or the extension f'v for all Bv).

L. D. Nel, Cartesian closed topological categories, Categorical Topology, Springer Leet. Notes in Math. 540 (1976) 439-451. L. D. Nel, Cartesian closed coreflective hulls, Quaest. Math. 2 (1977) 269-283. 26 18. 19. 20. 21. Ellen E. Reed, Nearnesses, proximities, and T1-compactifications, Trans. Amer. Math. Soc. 236 (1978) 193-207. W. A. Robertson, Convergence as a nearness concept, Thesis, Carleton Univ. (1975). A. K. Steiner and E. F. Steiner, On semi-uniformities, Fund. Math. 83 (1973) 47-58.

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Algebraic Topology and Tranformation Groups by Tammo tom Dieck

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