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Rad Hrvatske akademije znanosti i umjetnosti : Matematičke znanosti, No.532=21 Rujan 2017.

Izvorni znanstveni članak
https://doi.org/10.21857/9e31lh4nrm

Čech system does not induce approximate systems

Vlasta Matijević ; Department of Mathematics, Faculty of Science, University of Split, 21 000 Split, Croatia

Puni tekst: engleski, pdf (208 KB) str. 169-177 preuzimanja: 57* citiraj
APA 6th Edition
Matijević, V. (2017). Čech system does not induce approximate systems. Rad Hrvatske akademije znanosti i umjetnosti, (532=21), 169-177. https://doi.org/10.21857/9e31lh4nrm
MLA 8th Edition
Matijević, Vlasta. "Čech system does not induce approximate systems." Rad Hrvatske akademije znanosti i umjetnosti, vol. , br. 532=21, 2017, str. 169-177. https://doi.org/10.21857/9e31lh4nrm. Citirano 24.09.2018.
Chicago 17th Edition
Matijević, Vlasta. "Čech system does not induce approximate systems." Rad Hrvatske akademije znanosti i umjetnosti , br. 532=21 (2017): 169-177. https://doi.org/10.21857/9e31lh4nrm
Harvard
Matijević, V. (2017). 'Čech system does not induce approximate systems', Rad Hrvatske akademije znanosti i umjetnosti, (532=21), str. 169-177. doi: https://doi.org/10.21857/9e31lh4nrm
Vancouver
Matijević V. Čech system does not induce approximate systems. Rad Hrvatske akademije znanosti i umjetnosti [Internet]. 13.09.2017. [pristupljeno 24.09.2018.];(532=21):169-177. doi: https://doi.org/10.21857/9e31lh4nrm
IEEE
V. Matijević, "Čech system does not induce approximate systems", Rad Hrvatske akademije znanosti i umjetnosti, vol., br. 532=21, str. 169-177, rujan 2017. [Online]. doi: https://doi.org/10.21857/9e31lh4nrm

Sažetak
With every topological space X is associated its Čech system C(X)=(|N(U)|, [pUV], Cov(X)). It is well-known that the Čech system C(X) of X is an inverse system in the homotopy category HPol whose objects are polyhedra and morphisms are homotopy classes of continuous maps between polyhedra. We consider the following question posed by S. Mardešić. For a given Čech system (|N(U)|, [pUV], Cov(X)) of a space X, is it possible to select a member qUV ∈ [pUV] in each homotopy class [pUV] in such a way that the obtained system (|N(U)|, [qUV], Cov(X)) is an approximate system? We answer the question in the negative by proving that for each Hausdorff arc-like continuum X any such system (|N(U)|, [qUV], Cov(X)) is not an approximate system.

Ključne riječi
Inverse system; Čech system; approximate system; polyhedro; nerve of a covering; arc-like space; chainable space

Hrčak ID: 186436

URI
https://hrcak.srce.hr/186436

Posjeta: 89 *