17 citations · 21 across the 9 of their papers we have counts for
11 papers
A Descriptive Perspective on Devaney's Chaos and Some Results on Topologically Conjugate Systems
Fatih Ucan, Tane Vergili
In this study, Devaney's chaos conditions are revisited within the framework of descriptive proximity. The concepts of descriptive transitivity, the density of descriptive periodic…
Approximately Prime Rings and Prime Ideals
Maram Almahariq, James Francis Peters, Tane Vergili
This article focuses on approximately prime rings and approximately prime ideals in proximal relator spaces, especially in descriptive proximity spaces. In particular, we define so…
Indefinite Descriptive Proximities Inherent in Dynamical Systems. An Axiomatic Approach
James Francis Peters, Tane Vergili, Fatih Ucan +1
This paper introduces indefinite proximities inherent in the collection of physical objects found in a dynamical system. Axiomatically, these indefinite proximities lead to a new f…
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…
Fixed Point Property of Amenable Planar Vortexes
James F. Peters, Tane Vergili
This article introduces free group representations of planar vortexes in a CW space that are a natural outcome of results for amenable groups and fixed points found by M.M. Day dur…
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 $\D$…
Descriptive Fixed Set Properties for Ribbon Complexes
James F. Peters, Tane Vergili
This article introduces descriptive fixed sets and their properties in descriptive proximity spaces viewed in the context of planar ribbon complexes. These fixed sets are a byprodu…
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…