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
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
Datum izdavanja:
13.9.2017.
Posjeta: 954 *