7 papers
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…