Related papers: A construction of N\"obeling manifolds of arbitrar…

For a cardinal $\kappa > \omega$ a metric space $X$ is called to be $\kappa$-superuniversal whenever for every metric space $Y$ with $|Y| < \kappa$ every partial isometry from a subset of $Y$ into $X$ can be extended over the whole space…

For infinite cardinals $\kappa,\lambda$ let $C(\kappa,\lambda)$ denote the class of all compact Hausdorff spaces of weight $\kappa$ and size $\lambda$. So $C(\kappa,\lambda)=\emptyset$ if $\kappa>\lambda$ or $\lambda>2^\kappa$. If F is a…

Answering some of the main questions from [MR13], we show that whenever $\kappa$ is a cardinal satisfying $\kappa^{< \kappa} = \kappa > \omega$, then the embeddability relation between $\kappa$-sized structures is strongly invariantly…

In this note we begin a systematic study of compact conformal manifolds of SCFTs in four dimensions (our notion of compactness is with respect to the topology induced by the Zamolodchikov metric). Supersymmetry guarantees that such…

For any countable $CW$-complex $K$ and a cardinal number $\tau\geq\omega$ we construct a completely metrizable space $X(K,\tau)$ of weight $\tau$ with the following properties: $\e X(K,\tau)\leq K$, $X(K,\tau)$ is an absolute extensor for…

Let $M$ be a compact smooth manifold with corners and $N$ be a finite dimensional smooth manifold without boundary which admits local addition. We define a smooth manifold structure to general sets of continuous mapings $\mathcal{F}(M,N)$…

For certain uncountable cardinals $\kappa$ we produce a group of cardinality $\kappa$ which is freely indecomposable, strongly $\kappa$-free, and whose abelianization is free abelian of rank $\kappa$. The construction takes place in…

We use a natural forcing to construct a left-separated topology on an arbitrary cardinal kappa. The resulting left-separated space X_kappa is also 0-dimensional T_2, hereditarily Lindelof, and countably tight. Moreover if kappa is regular…

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…

Let B(kappa, lambda) be the subalgebra of P(kappa) generated by [kappa]^{<= lambda}. It is shown that if B is any homomorphic image of B(kappa, lambda) then either |B|< 2^lambda or |B|=|B|^lambda, moreover if X is the Stone space of B then…

We show that an embedding of a fixed 0-dimensional compact space $K$ into the \v{C}ech--Stone remainder $\omega^*$ as a nowhere dense P-set is the unique generic limit, a special object in the category consisting of all continuous maps from…

We introduce $\mathcal{B}_{\kappa}$-embeddings, nonlinear mathematical structures that connect, through smooth paths parameterized by $\kappa$, a finite or denumerable set of objects at $\kappa=0$ (e.g. numbers, functions, vectors,…

We consider the general problem of constructing the structure of a smooth manifold on a given space of loops in a smooth finite dimensional manifold. By generalising the standard construction for smooth loops, we derive a list of conditions…

We investigate 3-dimensional almost Kenmotsu manifolds satisfying special types of nullity conditions depending on two smooth functions $\kappa,\mu$. When either $\kappa<-1$ and $\mu=0$ or $h=0$, such conditions coincide with the…

Let $\kappa$ be an infinite cardinal. A topological space $X$ is $\kappa$-bounded if the closure of any subset of cardinality $\le\kappa$ in $X$ is compact. We discuss the problem of embeddability of topological spaces into Hausdorff…

The structure set $\ST^{TOP}(M)$ of an $n$-dimensional topological manifold $M$ for $n \geqslant 5$ has a homotopy invariant functorial abelian group structure, by the algebraic version of the Browder-Novikov-Sullivan-Wall surgery theory.…

For every n, we construct a metric measure space that is doubling, satisfies a Poincare inequality in the sense of Heinonen-Koskela, has topological dimension n, and has a measurable tangent bundle of dimension 1.

We show that if \kappa\ is a weakly compact cardinal then the embeddability relation on (generalized) trees of size \kappa\ is invariantly universal. This means that for every analytic quasi-order R on the generalized Cantor space 2^\kappa\…

We prove that for every uncountable cardinal $\kappa$ such that $\kappa^{<\kappa}=\kappa$, the quasi-order of embeddability on the $\kappa$-space of $\kappa$-sized graphs Borel reduces to the embeddability on the $\kappa$-space of…

We demonstrate that the technology of Radin forcing can be used to transfer compactness properties at a weakly inaccessible but not strong limit cardinal to a strongly inaccessible cardinal. As an application, relative to the existence of…