23 citations · 26 across the 3 of their papers we have counts for
6 papers
Stone duality for Kolmogorov locally small spaces
Artur Piękosz
We prove three new versions of Stone Duality. The main version is the following: the category of Kolmogorov locally small spaces and bounded continuous mappings is equivalent to th…
Bornological quasi-metrizability in generalized topology
Artur Piękosz, Eliza Wajch
A concept of quasi-metrizability with respect to a bornology of a generalized topological space in the sense of Delfs and Knebusch is introduced. Quasi-metrization theorems for gen…
Quasi-Metrizability of Bornological Biuniverses in ZF
A. Piękosz, E. Wajch
Hu's metrization theorem for bornological universes is shown to hold in ZF and it is adapted to a quasi-metrization theorem for bornologies in bitopological spaces. The problem of…
Compactness and compactifications in generalized topology
Artur Piȩkosz, Eliza Wajch
A generalized topology in a set is a collection of families of subsets of such that the triple is a generalized topol…
On generalized topological spaces
Artur Piȩkosz
In this paper a systematic study of the category GTS of generalized topological spaces (in the sense of H. Delfs and M. Knebusch) and their strictly continuous mappings begins. Som…
O-minimal homotopy and generalized (co)homology
Artur Piȩkosz
This article explains and extends semialgebraic homotopy theory (developed by H. Delfs and M. Knebusch) to o-minimal homotopy theory (over a field). The homotopy category of defina…