Related papers: Flimsy Spaces

Let $X$ be a locally compact topological space, $(Y,d)$ be a boundedly compact metric space and $LB(X,Y)$ be the space of all locally bounded functions from $X$ to $Y$. We characterize compact sets in $LB(X,Y)$ equipped with the topology of…

We determine the isomorphism classes of symmetric symplectic manifolds of dimension at least 4 which are connected, simply-connected and have a curvature tensor which has only one non-vanishing irreducible component -- the Ricci tensor.

Motivated by persistent homology and topological data analysis, we consider formal sums on a metric space with a distinguished subset. These formal sums, which we call persistence diagrams, have a canonical 1-parameter family of metrics…

We prove homological stability for sequences of "oriented configuration spaces" as the number of points in the configuration goes to infinity. These are spaces of configurations of n points in a connected manifold M of dimension at least 2…

Closure spaces are a generalisation of topological spaces obtained by removing the idempotence requirement on the closure operator. We adapt the standard notion of bisimilarity for topological models, namely Topo-bisimilarity, to closure…

Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…

A space is `n-arc connected' (n-ac) if any family of no more than n-points are contained in an arc. For graphs the following are equivalent: (i) 7-ac, (ii) n-ac for all n, (iii) continuous injective image of a closed sub-interval of the…

We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…

A topological space ${\mathcal X}$ is reversible iff each continuous bijection (condensation) $f: {\mathcal X} \rightarrow {\mathcal X}$ is a homeomorphism; weakly reversible iff whenever ${\mathcal Y}$ is a space and there are…

Metrizable spaces are studied in which every closed set is an $\alpha$-limit set for some continuous map and some point. It is shown that this property is enjoyed by every space containing sufficiently many arcs (formalized in the notion of…

A space has $\sigma$-compact tightness if the closures of $\sigma$-compact subsets determines the topology. We consider a dense set variant that we call densely k-separable. We consider the question of whether every densely k-separable…

We study the topology of the space of all smooth asymptotically stable vector fields on $\mathbb{R}^n$, as well as the space of all proper smooth Lyapunov functions for such vector fields. We prove that both spaces are path-connected and…

We prove that, on a compact almost complex manifold, the space of almost complex structures whose Nijenhuis tensor has rank at least $k$ at every point is either empty or dense in each path-connected component of the space of almost complex…

The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…

In the class of nonlinear one-parameter real maps we study those with bifurcation that exhibits period doubling cascade. The fixed points of such a map form a finite discrete real set with dimension (2^n)m, where m is the (odd) number of…

We construct several smooth finite element spaces defined on three--dimensional Worsey--Farin splits. In particular, we construct $C^1$, $H^1(\curl)$, and $H^1$-conforming finite element spaces and show the discrete spaces satisfy local…

This paper forms the third part of a series by the authors [GMV1,GMV2] concerning the structure theory of nilspaces. A nilspace is a compact space $X$ together with closed collections of cubes $C^n(X)\subseteq X^{2^n}$, $n=1,2,\ldots$,…

We use three seminal approaches in the study of fixed point theory, the so called $G$-metrics, multidimensional fixed points and partially ordered spaces. More precisely, we extend known results from the theory of quasi-pseudometric spaces…

We prove that the space of complete, finite volume, pinched negatively curved Riemannian metrics on a smooth high-dimensional manifold is either empty or it is highly non-connected, provided their behavior at infinity is similar.

We find an infinite number of noncommutative geometries which posses a differential structure. They generalize the two dimensional noncommutative plane, and have infinite dimensional representations. Upon applying generalized coherent…