Naslov
Coherent prohomotopy and strong shape theory

Autori
Lisica, Ju. T. ; Mardešić, Sibe

Izvornik
Glasnik matematički (0017-095X) 19 (1984), 2; 335-399

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
resolutions of a topological space ; coherent prohomotopy category ; coherent maps of systems ; coherent homotopy classes ; strong shape category ; ANR-resolutions

Sažetak
The coherent prohomotopy category CPHTop, defined in this paper, has as objects inverse systems X=(Xλ, pλλ′, Λ) of topological spaces and maps indexed by a directed cofinite index set Λ. To define morphisms f:X→Y=(Yμ, qμμ′, M) one first defines coherent maps of systems X→Y. These consist first of a function ϕ, which associates with each increasing sequence m=(m0, ..., mn) in M an element of Λ. Moreover, to every m it assigns a map fm:Xϕ(m)×Δn→Yμ0, with an appropriate behaviour with respect to the standard boundary and degeneracy operators between standard simplexes Δn. Morphisms of CPHTop are coherent homotopy classes of coherent maps. A special case of coherent maps is the case when ϕ(m)=ϕ(μn) and ϕ |M is increasing. Composition of the morphisms in CPHTop is defined by an explicit formula, which shows how to compose special coherent maps representing the given morphisms. The authors believe that the category CPHTop is isomorphic to the homotopy category of inverse systems considered in [D. A. Edwards and H. M. Hastings, Čech and Steenrod homotopy theories with applications to geometric topology, Lect. Notes Math. 542 (1976 ; Zbl 0334.55001)], the advantage consisting in its explicit geometric definition. Using the work of R. M. Vogt [Math. Z. 134, 11-52 (1973 ; Zbl 0276.55006)], T. Porter has a similar construction in [Cah. Topologie Géom. Différ. 19, 3-46 (1978 ; Zbl 0387.55013)].

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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