For any weightable quasi-metric space (X, d) having a maximum with respect to the associated order ≤d, the notion of the quasi-metric of complexity convergence on the the function space (equivalently, the space of sequences) X, is introduced and studied.We observe that its induced quasi-uniformity is finer than the quasi-uniformity of pointwise convergence and weaker than the quasi-uniformity o...

We prove uniqueness of instantaneously complete Ricci flows on surfaces. We do not require any bounds of any form on the curvature or its growth at infinity, nor on the metric or its growth (other than that implied by instantaneous completeness). Coupled with earlier work, particularly [25, 12], this completes the well-posedness theory for instantaneously complete Ricci flows on surfaces.

We show that for generic sliced spacetimes global hyperbolicity is equivalent to space completeness under the assumption that the lapse, shift and spatial metric are uniformly bounded. This leads us to the conclusion that simple sliced spaces are timelike and null geodesically complete if and only if space is a complete Riemannian manifold.

Bill Lawvere’s 1973 milestone paper “Metric spaces, generalized logic, and closed categories” helped us to detect categorical structures in previously unexpected surroundings. His revolutionary idea was not only to regard individual metric spaces as categories (enriched over the monoidal-closed category given by the non-negative extended real half-line, with arrows provided by ≥ and tensor by +...

In this paper, we study the generalized m-quasi-Einstein metric in context of contact geometry. First, prove if an H-contact manifold admits a with non-zero potential vector field V collinear ?, then M is K-contact and ?-Einstein. Moreover, it also true when H-contactness replaced by completeness under certain conditions. Next, that complete closed whose thenMis compact, Einstein Sasakian. Fina...

Asymptotic cones of metric spaces were first invented by Gromov. They are metric spaces which capture the ’large-scale structure’ of the underlying metric space. Later, van den Dries and Wilkie gave a more general construction of asymptotic cones using ultrapowers. Certain facts about asymptotic cones, like the completeness of the metric space, now follow rather easily from saturation propertie...

In this paper, we essentially deal with Köthe-Toeplitz duals of fuzzy level sets defined using a partial metric. Since the utilization of Zadeh's extension principle is quite difficult in practice, we prefer the idea of level sets in order to construct some classical notions. In this paper, we present the sets of bounded, convergent, and null series and the set of sequences of bounded variation...

This paper is to prove a common fixed point theorem for four self maps which generalizes the result of Brian Fisher [1] by a weaker conditions such as weakly compatible mappings and associated sequence instead of commuting mappings and completeness of a metric space.