Related papers: The topological structure of function space of tra…

We examine conditions on a (compact metrizable) space $X$ such that for any space $Y$ and closed subspace $Z$, the set of continuous functions from $Z$ to $X$ which extend to $Y$ is either open or closed in the set of continuous functions…

Let $t=t_1t_2\cdots$ be an element of the full shift with shift map $\tau$ on a finite set of characters $\mathcal{A}$ and let $ \Sigma=\text{ closure} \{\tau^i(t):\;i\in\N\cup\{0\}\}$. Let $f_t=f_{t_1,\,\infty}=\cdots\circ f_{t_2}\circ…

We give an upper bound for the topological entropy of maps on inverse limit spaces in terms of their set-valued components. In a special case of a diagonal map on the inverse limit space $\underleftarrow{\lim}(I,f)$, where every diagonal…

For a topological space $X$ a topological contraction on $X$ is a closed mapping $f:X\to X$ such that for every open cover of $X$ there is a positive integer $n$ such that the image of the space $X$ via the $n$th iteration of $f$ is a…

We show that the homeomorphism group of a surface without boundary does not admit a Hausdorff group topology strictly coarser than the compact-open topology. In combination with known automatic continuity results, this implies that the…

Let V, W be real algebraic varieties (that is, up to isomorphism, real algebraic sets), and let X be a subset of V. A map f from X into W is said to be regular if it can be extended to a regular map defined on some Zariski locally closed…

Let $S$ be a set of transpositions generating the symmetric group $S_n$. The transposition graph of $S$ is defined to be the graph with vertex set $\{1,\ldots,n\}$, and with vertices $i$ and $j$ being adjacent in $T(S)$ whenever $(i,j) \in…

Let $\pi$ be a discrete group, and let $G$ be a compact connected Lie group. $\mathrm{Hom}(\pi,G)_0$ denotes the null-component of the space of homomorphisms from $\pi$ to $G$, and $\mathrm{map}_*(B\pi,BG)_0$ denotes the null-component of…

A map $f:X\to Y$ between topological spaces is defined to be {\em scatteredly continuous} if for each subspace $A\subset X$ the restriction $f|A$ has a point of continuity. We show that for a function $f:X\to Y$ from a perfectly paracompact…

For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy is always finite. For compact manifolds of dimension two or greater, we show that in the closure of the space of bi-Lipschitz homeomorphisms, with…

The characteristic function has been an important tool for studying completely non unitary contractions on Hilbert spaces. In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space…

Given an autohomeomorphism on an ordered topological space or its subspace, we show that it is sometimes possible to introduce a new topology-compatible order on that space so that the same map is monotonic with respect to the new ordering.…

We study topologization of the semigroup $\mathscr{O\!\!I}\!_n(L)$ of finite partial order isomorphisms of a bounded rank of an infinite linear ordered set $(L,\leqslant)$. In particular we show that every $T_1$ left-topological…

For a topological space X, let (RX)s := (RX,Ts) be the cartesian product of |X| copies of the real line R with the topology of the uniform convergence on separable subsets of X. In this article we analyze the subspace C(X) of (RX)s of all…

Let $X$ and $Y$ be locally compact Hausdorff spaces. We denote by $C_0^+(X)$ the positive cone of all real-valued continuous functions on $X$ vanishing at infinity. In this paper, we consider a bijection $T\colon C_0^+(X) \to C_0^+(Y)$…

A map $X$ on a surface is called vertex-transitive if the automorphism group of $X$ acts transitively on the set of vertices of $X$. If the face-cycles at all the vertices in a map are of same type then the map is called semi-equivelar. In…

A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…

For the set C(X) of real-valued continuous functions on a Tychonoff space X, the compact-open topology on C(X) is a "set-open topology". This paper studies the separation and countability properties of the space C(X) having the topology…

We construct a locally compact Hausdorff topology on the path space of a directed graph $E$, and identify its boundary-path space $\partial E$ as the spectrum of a commutative $C^*$-subalgebra $D_E$ of $C^*(E)$. We then show that $\partial…

If $\mathcal P$ is a family of filters over some set $I$, a topological space $X$ is \emph{sequencewise $\mathcal P$-\brfrt compact} if, for every $I$-indexed sequence of elements of $X$, there is $F \in \mathcal P$ such that the sequence…