Related papers: Embedding measure spaces

Let $(\mathcal{X},\rho)$ be a metric space and $\lambda$ be a Borel measure on this space defined on the $\sigma$-algebra generated by open subsets of $\mathcal{X}$; this measure $\lambda$ defines volumes of Borel subsets of $\mathcal{X}$.…

In this paper, we have proved results similar to Tychonoff's Theorem on embedding a space of functions with the topology of pointwise convergence into the Tychonoff product of topological spaces, but applied to the function space $C(X,Y)$…

Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a…

Let M be a PL 2-manifold and X be a compact subpolyhedron of M and let E(X, M) denote the space of embeddings of X into M with the compact-open topology. In this paper we study an extension property of embeddings of X into M and show that…

We prove that if $X$ is a topological space that admits Debreu's classical utility theorem (eg.\ $X$ is separable and connected, second countable, etc.), then order relations on $X$ satisfying milder completeness conditions can be…

By taking the complements of embeddings of sphere plumbings in connected sums of $\mathbb{C} P^2$, we construct examples of simply connected four-manifolds with lens space boundary and $b_2 = 1$. The resulting boundaries include many lens…

Any planar shape $P\subset \mathbb{C}$ can be embedded isometrically as part of the boundary surface $S$ of a convex subset of $\mathbb{R}^3$ such that $\partial P$ supports the positive curvature of $S$. The complement $Q = S \setminus P$…

If $X$ is an analytic metric space satisfying a very mild doubling condition, then for any finite Borel measure $\mu$ on $X$ there is a set $N\subseteq X$ such that $\mu(N)>0$, an ultrametric space $Z$ and a Lipschitz bijection $\phi:N\to…

Let $M$ be a compact 1-manifold. Given a continuous function $g:M\to \mathbb R_+$ we consider the following ordinary differential equation: $\|\dot{f}(t)\|=g(t)$, where $f:M\to \mathbb R^2$. We construct a probability measure on the space…

The possibility of extending operations of topological and semitopological algebras to their Stone-\v{C}ech compactification and factorization of continuous functions through homomorphisms to metrizable algebras are investigated. Most…

The group-theoretic method for constructing symmetric isometric embeddings is used to describe all possible four-dimensional surfaces in flat $(1,9)$-dimensional space, whose induced metric is static and spherically symmetric. For such…

This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…

Let $X$ be a projective toric variety of dimension $n$ and let $L$ be a ample line bundle on $X$. For $k \geq 0$, it is in general difficult to determine whether $L^{\otimes k}$ is very ample and whether it additionally gives a projectively…

We study completeness of a topological vector space with respect to different filters on the set N of all naturals. In the metrizable case all these kinds of completeness are the same, but in non-metrizable case the situation changes. For…

This report introduces and investigates a family of metrics on sets of pointed Kripke models. The metrics are generalizations of the Hamming distance applicable to countably infinite binary strings and, by extension, logical theories or…

Let $X$ be a separable nonquasireflexive Banach space. Let $Y$ be a Banach space isomorphic to a subspace of $X^*$. The paper is devoted to the following questions: 1. Under what conditions does there exist an isomorphic embedding $T:Y\to…

When $X$ is locally compact, a quasi-integral (also called a quasi-linear functional) on $ C_c(X)$ is a homogeneous, positive functional that is only assumed to be linear on singly-generated subalgebras. We study simple and almost simple…

For a metrizable space $X$ of density $\kappa$, let $PM(X)$ be the space of continuous bounded pseudometrics on $X$ endowed with the uniform convergence topology. In this paper, its topology shall be classified as follows: (i) If $X$ is…

Characterisations of metrizable topological spaces or metrizable uniform spaces are well known. A natural counterpart to being metrizable for topological spaces can be expressed in terms of probabilistic metrizability for approach spaces.…

We consider a smooth closed orientable submanifold $M \subset \mathbb{R}^D$ with narrow cycles. We embed $M$ into a scaled oriented Grassmannian bundle via the Gauss map in order to enlarge the scale of these cycles. Under mild assumptions,…