Related papers: Continuous mappings between spaces of arcs

For any compact, connected, orientable, finite-type surface with marked points other than the sphere with three marked points, we construct a finite rigid set of its arc complex: a finite simplicial subcomplex of its arc complex such that…

Using sheaf theory, I introduce a continuous theory of persistence for mappings between compact manifolds. In the case both manifolds are orientable, the theory holds for integer coefficients. The sheaf introduced here is stable to…

This article deals with homomorphisms of oriented graphs with respect to push equivalence. Here homomorphisms refer to arc preserving vertex mappings, and push equivalence refers to the equivalence class of orientations of a graph $G$ those…

We consider all compatible topologies of an arbitrary finite-dimensional vector space over a non-trivial valuation field whose metric completion is a locally compact space. We construct the canonical lattice isomorphism between the lattice…

For metrizable spaces we replace the notion of almost periodic homeomorphism with a similar notion and verify that the usual characterizations of almost periodic homeomorphisms of compact metric spaces are valid for all metrizable spaces.

In this study, we present a concept of morphing structure -- featuring an arch mounted on a compliant base -- that can be reconfigured via snap-through buckling and leverages bistability to retain its morphed shape. We show that…

For a symplectic twist map, we prove that there is a choice of weak K.A.M. solutions that depend in a continuous way on the cohomology class. We thus obtain a continuous function $u(\theta, c)$ in two variables: the angle $\theta$ and the…

We study uniform and coarse embeddings between Banach spaces and topological groups. A particular focus is put on equivariant embeddings, i.e., continuous cocycles associated to continuous affine isometric actions of topological groups on…

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

We find an arc-parameterization of the contour on which an given analytic function has constant modulus. This contour is seen to satisfy a differential equation which we explicitly give.

A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous superpositions. Associated to a given continuous frame we construct certain Banach spaces. Many classical function…

In this paper, we study the deformation of the intersection of one compact set with a closed neighborhood of another compact set by changing the radius of this neighborhood. It is shown that in finite-dimensional normed spaces, in the case…

Tension-continuous (shortly TT) mappings are mappings between the edge sets of graphs. They generalize graph homomorphisms. From another perspective, tension-continuous mappings are dual to the notion of flow-continuous mappings and the…

In this paper, we show that some fundamental results for smooth mappings (e.g., the Brouwer degree formula, the implicit function and inverse function theorems, the mean value theorem, Sard's theorem, Hadamard's global invertibility…

A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…

The moduli space of stable relative maps to the projective line combines features of stable maps and admissible covers. We prove all standard Gromov-Witten classes on these moduli spaces of stable relative maps have tautological…

We show that if a group automorphism of a Cremona group of arbitrary rank is also a homeomorphism with respect to either the Zariski or the Euclidean topology, then it is inner up to a field automorphism of the base-field. Moreover, we show…

Argument graphs provide an abstract representation of an argumentative situation. A bipolar argument graph is a directed graph where each node denotes an argument, and each arc denotes the influence of one argument on another. Here we…

There are several Teichm\"uller spaces associated to a surface of infinite topological type, after the choice of a particular basepoint (a complex or a hyperbolic structure on the surface). These spaces include the quasiconformal…

We study the invariant measures of typical $C^0$ maps on compact connected manifolds with or without boundary, and also of typical homeomorphisms. We prove that the weak$^*$ closure of the set of ergodic measurescoincides with the weak$^*$…