4 citations · 4 across the 7 of their papers we have counts for
6 papers · 1 filter
Connectedness, Continuity, and Proximities in Temporal Digital Topology
James Francis Peters, Tane Vergili
This paper introduces the structure and axioms for a temporal digital topology (TDT) with the focus on digital connectedness, continuity and proximities in TDT spaces. Results are…
Good Coverings of Proximal Alexandrov Spaces. Homotopic Cycles in Jordan Curve Theorem Extension
J. F. Peters, T. Vergili
This paper introduces proximal homotopic cycles, which lead to the main results in this paper, namely, extensions of the Mitsuishi-Yamaguchi Good Coverning Theorem with different f…
Contiguity Distance between Simplicial Maps
Ayse Borat, Mehmetcik Pamuk, Tane Vergili
We study properties of contiguity distance between simplicial maps. In particular, we show that simplicial versions of -category and topological complexity are particular cases…
Topological spaces induced by homotopic distance
Tane Vergili, Ayse Borat
Homotopic distance $\D$ as introduced in \cite{MVML} can be realized as a pseudometric on . In this paper, we study the topology induced by the pseudometric $\D$…
Higher Homotopic Distance
Ayse Borat, Tane Vergili
The concept of homotopic distance and its higher analog are introduced in [6]. In this paper we introduce some important properties of higher homotopic distance, investigate the co…
Topological spaces of persistence modules and their properties
Peter Bubenik, Tane Vergili
Persistence modules are a central algebraic object arising in topological data analysis. The notion of interleaving provides a natural way to measure distances between persistence…