Related papers: On perturbations of continuous maps
Let $f \colon X \rightarrow Y$ be a resolvable-measurable mapping of a metrizable space $X$ to a regular space $Y$. Then $f$ is piecewise continuous. Additionally, for a metrizable completely Baire space $X$, it is proved that $f$ is…
If a continuous map f: X->Q is approximable arbitrary closely by embeddings X->Q, can some embedding be taken onto f by a pseudo-isotopy? This question, called Isotopic Realization Problem, was raised by Shchepin and Akhmet'ev. We consider…
In this paper some new cases of Knaster's problem on continuous maps from spheres are established. In particular, we consider an almost orbit of a $p$-torus $X$ on the sphere, a continuous map $f$ from the sphere to the real line or real…
Consider a Hausdorff space (X,T) and a set C of converging nets in X. By virtue of the limit uniqueness, the relation Lim which assigns each member x of X to every net N lying in C that converges to x is a map. Of course, structuring C with…
The larger the distance to instability from a matrix is, the more robustly stable the associated autonomous dynamical system is in the presence of uncertainties and typically the less severe transient behavior its solution exhibits.…
We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.
We begin the study of the consequences of the existence of certain infinite matrices. Our present application is to compactness of products of topological spaces.
Homotopic distance $\D$ as introduced in \cite{MVML} can be realized as a pseudometric on $\mathrm{Map}(X,Y)$. In this paper, we study the topology induced by the pseudometric $\D$. In particular, we consider the space…
The variation of spectral subspaces for linear self-adjoint operators under an additive bounded off-diagonal perturbation is studied. To this end, the optimization approach for general perturbations in [J. Anal. Math., to appear;…
We introduce a bivariate version of topological complexity, $\mathrm{TC}(f,g)$, associated with two continuous maps $f\colon X\to Z$ and $g\colon Y\to Z$. This invariant measures the minimal number of continuous motion planning rules…
It is investigated the existence of a separately continuous function $f:X\times Y\to \mathbb R$ with an onepoint set of discontinuity for topological spaces $X$ and $Y$ which satisfy compactness type conditions. In particular, it is shown…
We construct a family F of compact and pathwise connected subsets of the Euclidean plane such that (i) the cardinality of F is that of the continuum (and hence extremely large) and (ii) if X,Y are distinct spaces in F then there never…
In this letter we proved this theorem: \emph{if $F$ be a holomorphic mapping of $T_{\Omega}$ to a mapping manifold $X$ such that for every compact subset $K\subset \Omega$ the mapping $F$ is uniformly continues on $T_{K}$ and $F(T_{K})$ is…
This paper investigates the effects that perturbations to an optical system, such as translations or rotations of the optical elements, have on the final location where a light ray strikes a detector. Symmetry arguments are employed to give…
We consider the maximal number of arbitrary points in a special fibre that can be simultaneously approached by points in one sequence of general fibres. Several results about this topological invariant and their applications describe the…
Given a diagonalizable matrix $A$, we study the stability of its invariant subspaces when its matrix of eigenvectors is ill-conditioned. Let $\mathcal{X}_1$ be some invariant subspace of $A$ and $X_1$ be the matrix storing the right…
Let $C$ be a convex subset of a locally convex space. We provide optimal approximate fixed point results for sequentially continuous maps $f\colon C\to\bar{C}$. First we prove that if $f(C)$ is totally bounded, then it has an approximate…
We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are…
A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional…
We consider a class of graphs subject to certain restrictions, including the finiteness of diameters. Any surjective mapping $\phi:\Gamma\to\Gamma'$ between graphs from this class is shown to be an isomorphism provided that the following…