Related papers: Nonseparably connected complete metric spaces

We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold $M$ is…

Inspired by group cohomology, we define several coarse topological invariants of metric spaces. We define the coarse cohomological dimension of a metric space, and demonstrate that if G is a countable group, then the coarse cohomological…

We prove that a countably compact space is monotonically retractable if and only if it has a full retractional skeleton. In particular, a compact space is monotonically retractable if and only if it is Corson. This gives an answer to a…

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…

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision…

In this short note, we show that, in any given metric space, every Lipschitz open-map image of every subset of a given metric space whose boundary is Hausdorff-null is Hausdorff-measurable with respect to the same dimension. The main…

For a locally path connected topological space, the topological fundamental group is discrete if and only if the space is semilocally simply-connected. While functoriality of the topological fundamental group for arbitrary topological…

Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…

For every space $X$ let $\mathcal K(X)$ be the set of all compact subsets of $X$. Christensen \cite{c:74} proved that if $X, Y$ are separable metrizable spaces and $F\colon\mathcal{K}(X)\to\mathcal{K}(Y)$ is a monotone map such that any…

If $X$ is a (topological) space, the $n$th finite subset space of $X$, denoted by $X(n)$, consists of $n$-point subsets of $X$ (i.e., nonempty subsets of cardinality at most $n$) with the quotient topology induced by the unordering map…

In this paper we give conditions under which a topological semigroup can be embedded algebraically and topologically into a compact topological group. We prove that every feebly compact regular first countable cancellative commutative…

Let $X$ be a topological space and $f:X\to X$ a bijection. Let ${\mathcal C}(X,f)$ be a set of integers such that an integer $n$ is an element of ${\mathcal C}(X,f)$ if and only if the bijection $f^n:X\to X$ is continuous. A subset $S$ of…

We study the topology of the space of harmonic maps from $S^2$ to \CP 2$. We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for…

A topological group $X$ is called connected if the only subsets which are both open and closed are the whole space $X$ and the null set $\emptyset$. A subset of a topological group is connected if the subspace is connected. We say that a…

We show that there is a compact topological space carrying a measure which is not a weak* limit of finitely supported measures but is in the sequential closure of the set of such measures. We construct compact spaces with measures of…

we prove that if $X$ is a locally compact $\sigma$-compact space then on its quotient, $\gamma(X)$ say, determined by the algebra of all real valued bounded continuous functions on $X$, the quotient topology and the completely regular…

We show that if there exists a topologically expansive homeomorphism on a uniform space, then the space is always a regular space. Through examples we show that in general composition of topologically expansive homeomorphisms need not be…

We show that any metacompact Moore space is monotonically metacompact and use that result to characterize monotone metacompactness in certain generalized ordered (GO)spaces. We show, for example, that a generalized ordered space with a…

A generalization of metric space is presented which is shown to admit a theory strongly related to that of ordinary metric spaces. To avoid the topological effects related to dropping any of the axioms of metric space, first a new, and…

In this note we study some properties of topological entropy for non-compact non-metrizable spaces. We prove that if a uniformly continuous self-map $f$ of a uniform space has topological shadowing property then the map $f$ has positive…