Related papers: Some topological and combinatorial properties pres…
Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…
Inversion of various inclusions, that characterize continuity in topological spaces, results in numerous variants of quotient and perfect maps. In the framework of convergences, the said inclusions are no longer equivalent, and each of them…
We study the variational behavior of the total inverse mean curvature of curves with prescribed boundary in the half-plane. We characterize the existence of critical points with prescribed area. We show that such critical points are…
Given a compact metric space $X$, we associate to it an inverse sequence of finite $T_0$ topological spaces. The inverse limit of this inverse sequence contains a homeomorphic copy of $X$ that is a strong deformation retract. We provide a…
Topological aspects represent currently a boosting area in condensed matter physics. Yet there are very few suggestions for technical applications of topological phenomena. Still, the most important is the calibration of resistance…
We prove that multiple-recurrence and polynomial-recurrence of invertible infinite measure preserving transformations are both properties which pass to extensions.
Adapting a homotopy reconstruction theorem for general metric compacta, we show that every countable metric or ultrametric compact space can be topologically reconstructed as the inverse limit of a sequence of finite $T_0$ spaces which are…
Examples are given of q-deformed systems that may be interpreted by the standard rules of quantum theory in terms of new degrees of freedom and supplementary quantum numbers.
We look at the preservation of various notions of shadowing in discrete dynamical systems under inverse limits, products, factor maps and the induced maps for symmetric products and hyperspaces. The shadowing properties we consider are the…
An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Frechetness, strong Frechetness,…
Varieties of the Fan Theorem have recently been developed in reverse constructive mathematics, corresponding to different continuity principles. They form a natural implicational hierarchy. Some of the implications have been shown to be…
A generic method for combinatorial constructions of intrinsic geometrical spaces is presented. It is based on the well known inverse sequences of finite graphs that determine (in the limit) topological spaces. If a pattern of the…
In this paper we define contractive and nonexpansive properties for adapted stochastic processes $X_1, X_2, \ldots $ which can be used to deduce limiting properties. In general, nonexpansive processes possess finite limits while contractive…
We introduce a framework for internal topological symmetries in quantum field theory, including "noninvertible symmetries" and "categorical symmetries". This leads to a calculus of topological defects which takes full advantage of…
The generalized divided differences are introduced. They are applied to investigate some properties characterizing generalized higher-order convexity. Among others some support-type property is proved.
Numerous properties of vector addition systems with states amount to checking the (un)boundedness of some selective feature (e.g., number of reversals, run length). Some of these features can be checked in exponential space by using…
We prove a geometric property of the set A^{-1} of inverses of the nonzero elements of an F_q-subspace A of a finite field involving the size of its intersection with two-dimensional F_q-subspaces. We give some applications, including a new…
We explore various combinatorial problems mostly borrowed from physics, that share the property of being continuously or discretely integrable, a feature that guarantees the existence of conservation laws that often make the problems…
We prove that various spaces of constrained positive scalar curvature metrics on compact 3-manifolds with boundary, when not empty, are contractible. The constraints we mostly focus on are given in terms of local conditions on the mean…
We prove special cases of a general conjecture: If an invertible field theory admits a projectively topological boundary theory, then it has finite order in the abelian group of invertible field theories. One can substitute `gapped' for…