Glasnik matematički, Vol. 52 No. 2, 2017.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.52.2.01
On the inverse limits of T0-Alexandroff spaces
Paweł Bilski
orcid.org/0000-0003-3044-6049
; Institute of Mathematics, Polish Academy of Sciences, 00-656 Warsaw, Poland
Sažetak
We show that if X is a locally compact, paracompact and Hausdorff space, then X can be realised as the subspace of all maximal points of the inverse limit of an inverse system of partial orders with an appropriate topology (equivalently T0-Alexandroff spaces). Then, the space X is homeomorphic to a deformation retract of that limit. Moreover, we extend results obtained by Clader and Thibault and show that if K is a simplicial complex, then its realisation |K| can be obtained as the subspace of all maximals of the limit of an inverse system of T0-Alexandroff spaces such that each of them is weakly homotopy equivalent to |K|. Moreover, if K is locally-finite-dimensional and |K| is considered with the metric topology, then this inverse system can be replaced by an inverse sequence.
Ključne riječi
Alexandroff space; inverse limit; locally compact space; paracompact space; partial order; simplicial complex; weak homotopy type
Hrčak ID:
189327
URI
Datum izdavanja:
13.11.2017.
Posjeta: 1.338 *