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Strong shape theory and resolutions. (English) Zbl 0505.55012


MSC:

55P55 Shape theory
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
54C55 Absolute neighborhood extensor, absolute extensor, absolute neighborhood retract (ANR), absolute retract spaces (general properties)
54C56 Shape theory in general topology
55U35 Abstract and axiomatic homotopy theory in algebraic topology
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References:

[1] Borsuk, K., Theory of Retracts, (Monographie Matematyczne, 44 (1967), PWN: PWN Warszawa) · Zbl 0153.52905
[2] Cathey, F. W., Strong shape theory, (Ph.D. Thesis (1979), University of Washington) · Zbl 0588.55008
[3] Cathey, F. W., Strong shape theory, (Shape Theory and Geometric Topology Proc. (Dubrovnik, 1981). Shape Theory and Geometric Topology Proc. (Dubrovnik, 1981), Lecture Notes in Math., 870 (1981), Springer-Verlag: Springer-Verlag Berlin), 215-238 · Zbl 0588.55008
[4] Calder, A.; Hastings, H. M., Realizing strong shape equivalences, J. Pure Appl. Algebra, 20, 129-156 (1981) · Zbl 0457.55004
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[8] Gabriel, P.; Zisman, M., Calculus of fractions and homotopy theory, (Ergebnisse der Matematik, 35 (1967), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0186.56802
[9] Kodama, Y.; Ono, J., On fine shape theory, Fund. Math., 105, 29-39 (1979) · Zbl 0425.54016
[10] Mardešić, S., Shapes for topological spaces, Gen. Topology Appl., 3, 265-282 (1973) · Zbl 0269.55008
[11] Mardešić, S., Inverse limits and resolutions, (Shape Theory and Geometric Topology Proc. (Dubrovnik, 1981). Shape Theory and Geometric Topology Proc. (Dubrovnik, 1981), Lecture Notes in Math., 870 (1981), Springer-Verlag: Springer-Verlag Berlin), 239-252
[12] Mardešić, S., Approximate polyhedra, resolutions of maps, and shape fibrations, Fund. Math., 114, 53-78 (1981) · Zbl 0411.54019
[13] Mardešić, S.; Segal, J., Shape theory (1982), North-Holland: North-Holland Amsterdam · Zbl 0495.55001
[14] Quigley, J. B., An exact sequence from the \(n\) th to the \((n-1)\)-st fundamental group, Fund. Math., 77, 195-210 (1973) · Zbl 0247.55010
[15] Quillen, D. G., Homotopical Algebra, (Lecture Notes in Math., 43 (1967), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0168.20903
[16] Spanier, E., Algebraic Topology (1966), McGraw-Hill: McGraw-Hill New York · Zbl 0145.43303
[17] Str∅m, A., The homotopy category is a homotopy category, Arc. Math., 23, 435-441 (1973), (Basel)
[18] Str∅m, A., Note on cofibrations II, Math. Scand., 22, 130-142 (1968) · Zbl 0181.26504
[19] Vogt, R. M., Homotopy limits and colimits, Math. Z., 134, 11-52 (1973) · Zbl 0276.55006
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