Related papers: Comparing topologies on linearly recursive sequenc…
Topological recursion associates to a spectral curve, a sequence of meromorphic differential forms. A tangent space to the "moduli space" of spectral curves (its space of deformations) is locally described by meromorphic 1-forms, and we use…
In this paper we have shown that a double sequence in a topological space satisfies certain conditions which in turn are capable to generate a topology on a non empty set. Also we have used the idea of I-convergence of double sequences to…
Even in spaces of formal power series is required a topology in order to legitimate some operations, in particular to compute infinite summations. Many topologies can be exploited for different purposes. Combinatorists and algebraists may…
Linear topological spaces with partial ordering (linear kinematics) are studied. They are defined by a set of 8 axioms implying that topology, linear structure and ordering are compatible with each other. Most of the results are valid for…
In this paper, we obtain some results on the relationships between different ideal \linebreak convergence modes namely, $\mathcal{I}^\mathcal{K}$, $\mathcal{I}^{\mathcal{K}^*}$, $\mathcal{I}$, $\mathcal{K}$, $\mathcal{I} \cup \mathcal{K}$…
Given a spectral curve with exponential singularities (which we call a "transalgebraic spectral curve"), we extend the definition of topological recursion to include contributions from the exponential singularities in a way that is…
We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are…
For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of…
The union of a directed family of topological groups can be equipped with two noteworthy topologies: the finest topology making each injection continuous, and the finest group topology making each injection continuous. This begs the…
The topology of weak convergence does not account for the growth of information over time that is captured in the filtration of an adapted stochastic process. For example, two adapted stochastic processes can have very similar laws but give…
An intersection of sets $A = \bigcap_{i \in I}B_i$ is irredundant if no $B_i$ can be omitted from this intersection. We develop a topological approach to irredundance by introducing a notion of a spectral representation, a spectral space…
Towards building tropical analogues of adic spaces, we study certain spaces of prime congruences as a topological semiring replacement for the space of continuous valuations on a topological ring. This requires building the theory of…
This article belongs to a subject, Directed Algebraic Topology, whose general aim is including non-reversible processes in the range of topology and algebraic topology. Here, as a further step, we also want to cover "critical processes",…
We introduce two novel concepts, topological difference and topological correlation, that offer a new perspective on the discriminative power of multiparameter persistence. The former quantifies the discrepancy between multiparameter and…
We present a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the predicate calculus as well as a formal induction principle. We introduce recursive systems generating…
We introduce a topology, which we call the regional topology, on the space of all real functions on a given locally compact metric space. Next we obtain a new versions of Schauder's fixed point theorem and Ascoli's theorem. We use these…
Ordinary maps satisfy topological recursion for a certain spectral curve $(x, y)$. We solve a conjecture from arXiv:1710.07851 that claims that fully simple maps, which are maps with non self-intersecting disjoint boundaries, satisfy…
We investigate formal power series ideals and their relationship to topological rewriting theory. Since commutative formal power series algebras are Zariski rings, their ideals are closed for the adic topology defined by the maximal ideal…
Two classes of topological spaces are introduced on which every probability Radon measure possesses a uniformly distributed sequence or a uniformly tight uniformly distributed sequence. It is shown that these classes are stable under…
In many areas of applied geometric/numeric computational mathematics, including geo-mapping, computer vision, computer graphics, finite element analysis, medical imaging, geometric design, and solid modeling, one has to compute incidences,…