Related papers: Skeletally Dugundji spaces

We prove the existence of a simultaneous projectional skeleton for certain subspaces of $\mathcal{C}(K)$ spaces. This generalizes a result on simultaneous projectional resolutions of identity proved by M. Valdivia. We collect some…

We say that a finite metric space $X$ can be embedded almost isometrically into a class of metric spaces $C$, if for every $\epsilon > 0$ there exists an embedding of $X$ into one of the elements of $C$ with the bi-Lipschitz distortion less…

The moduli space of triangles is a two-dimensional space that records triangle shapes in the plane, considered up to similarity. We study the subset corresponding to \textit{lattice triangles}, which are triangles whose vertices have…

Let X = G/P be a cominuscule rational homogeneous variety. (Equivalently, X admits the structure of a compact Hermitian symmetric space.) I give a uniform description (that is, independent of type) of the irreducible components of the…

Let X be a path connected, compact metric space and let A be a unital separable simple nuclear Z-stable real rank zero C*-algebra. We classify all the unital *-embeddings (up to approximate unitary equivalence) of C(X) into A. Specifically,…

Let X be a symmetric space of non-compact type or a locally finite, strongly transitive Euclidean building, and let B denote the geodesic boundary of X. We reduce the study of visual limits of maximal flats in X to the study of limits of…

We find a one-to-one correspondence between full extrinsic symmetric spaces in (possibly degenerate) inner product spaces and certain algebraic objects called (weak) extrinsic symmetric triples. In particular, this yields a description of…

For a Tychonoff space $X$, let $C_k(X)$ and $C_p(X)$ be the spaces of real-valued continuous functions $C(X)$ on $X$ endowed with the compact-open topology and the pointwise topology, respectively. If $X$ is compact, the classic result of…

To each simplicial set $X$ we naturally assign an \'etendue ${\'E X}$ whose internal logic captures information about the geometry of $X$. In particular, we show that, for 'non-singular' objects $X$ and $Y$, the \'etendues ${\'E X}$ and…

A compact space $X$ is said to be minimal if there exists a map $f:X\to X$ such that the forward orbit of any point is dense in $X$. We consider rigid minimal spaces, motivated by recent results of Downarowicz, Snoha, and Tywoniuk [J. Dyn.…

An $r$-skeleton on a compact space is a family of continuous retractions having certain rich properties. The $r$-skeletons have been used to characterized the Valdivia compact spaces and the Corson compact spaces. Here, we characterized a…

All spaces are assumed to be Tychonoff. Given a realcompact space $X$, we denote by $\mathsf{Exp}(X)$ the smallest infinite cardinal $\kappa$ such that $X$ is homeomorphic to a closed subspace of $\mathbb{R}^\kappa$. Our main result shows…

The paper deals with Ascoli spaces $C_p(X)$ and $C_k(X)$ over Tychonoff spaces $X$. The class of Ascoli spaces $X$, i.e. spaces $X$ for which any compact subset $K$ of $C_k(X)$ is evenly continuous, essentially includes the class of…

We state several sufficient conditions for compact spacelike surface in the3-dimensional de Sitter space to be totally geodesic or spherical.

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…

This paper gives a uniform-theoretic refinement of classical homotopy theory. Both cubical sets (with connections) and uniform spaces admit classes of weak equivalences, special cases of classical weak equivalences, appropriate for the…

We prove that any separable AM-space $X$ has an equivalent lattice norm for which no non-trivial surjective lattice isometries exist. Moreover, if $X$ has no more than one atom, then this new norm may be an AM-norm. As our main tool, we…

A space $X$ is said to be $\pi$-metrizable if it has a $\sigma$-discrete $\pi$-base. In this paper, we mainly give affirmative answers for two questions about $\pi$-metrizable spaces. The main results are that: (1) A space $X$ is…

Let $X$ and $S$ be complex spaces with $X$ countable at infinity and $S$ reduced locally pure dimensional. Let $\pi:X\to S$ be an universally-$n$-equidimensional morphism (i.e open with constant pure $n$-dimensional fibers). If there is a…

We discuss all possible compactifications on flat three-dimensional smooth spaces. In particular, various fields are studied on a box with opposite sides identified, after two of them are rotated by $\pi$, and their spectra are obtained.…