An Introduction to Algebraic Topology by Andrew H. Wallace

By Andrew H. Wallace

This self-contained remedy assumes just some wisdom of genuine numbers and actual research. the 1st 3 chapters specialise in the fundamentals of point-set topology, and then the textual content proceeds to homology teams and non-stop mapping, barycentric subdivision, and simplicial complexes. routines shape an essential component of the textual content. 1961 variation.

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D. J. , 1 (1971), 43-48. 8. E. A. Michael, No-S~aces , J. Math. , 15 (1956), 983-1002. 9. J. Nagata and F. Siwiec, A note on nets and metrization, Proc. , 44 (1968), 623-627. W. Heath and R. H. Hodel, Characterizations of o-spaces, Fund. Math. 77 (1973), 271-275. i0. A. Okuyama, Some seneralizations of metric spaces, their metrization theorems and product theorems, Sci. Rep. Tokyo Kyioku Daigaku Sect. A, 9 (1967), 234-254. ii. P. O'Meara, A new class of topolo$ical spaces, University of Alberta dissertation, 1966.

178 (1973), 481-494. 6. N. Lasnev, Continuous decompositions and closed mappings of metric spaces, Sov. Math. , 6 (1965), 1504-1506. 7. D. J. , 1 (1971), 43-48. 8. E. A. Michael, No-S~aces , J. Math. , 15 (1956), 983-1002. 9. J. Nagata and F. Siwiec, A note on nets and metrization, Proc. , 44 (1968), 623-627. W. Heath and R. H. Hodel, Characterizations of o-spaces, Fund. Math. 77 (1973), 271-275. i0. A. Okuyama, Some seneralizations of metric spaces, their metrization theorems and product theorems, Sci.

Throughout this paper we will restrict ourselves to finite CW complexes. For infor- mation about the locally-finite case we refer the reader to [5]. A Hilbert cube manifold (or Q-manifold) open cover by sets that are homeomorphic is a separable metric space having an to open subsets of Q. is a space X for which X X Q is a Q-manifold. A Q-manifold factor It is clear that every finite-dimen- sional n-manifold is a Q-manifold factor and West has shown that every finite CW complex is a Q-manifold factor [ii].

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