43 citations · 238 across the 28 of their papers we have counts for
7 papers · 1 filter
Approximations of 1-Dimensional Intrinsic Persistence of Geodesic Spaces and Their Stability
Žiga Virk
A standard way of approximating or discretizing a metric space is by taking its Rips complexes. These approximations for all parameters are often bound together into a filtration,…
1-Dimensional Intrinsic Persistence of Geodesic Spaces
Žiga Virk
Given a compact geodesic space we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or Čech filtration of to obtain w…
Higson Compactification and Dimension Raising
Kyle Austin, Žiga Virk
Let and be proper metric spaces. We show that a coarsely -to- map induces an -to- map of Higson coronas. This viewpoint turns out to be success…
On semilocally simply connected spaces
Hanspeter Fischer, Dušan Repovš, Ziga Virk +1
The purpose of this paper is: (i) to construct a space which is semilocally simply connected in the sense of Spanier even though its Spanier group is non-trivial; (ii) to propose a…
Homotopical Smallness and Closeness
Ziga Virk
The aim of this paper is to introduce the concepts of homotopical smallness and closeness. These are the properties of homotopical classes of maps that are related to recent develo…
Realizations of Countable Groups as Fundamental Groups of Compacta
Ziga Virk
It is an open question (Pawlikowski) whether every finitely generated group can be realized as a fundamental group of a compact metric space. In this paper we prove that any counta…