Related papers: N^N^N does not satisfy Normann's condition

For a target variety $X$ and a nodal curve $C$, we introduce a one-parameter stability condition, termed $\epsilon$-admissibility, for maps from nodal curves to $X\times C$. If $X$ is a point, $\epsilon$-admissibility interpolates between…

Let $|\cdot|$ be the standard Euclidean norm on $\mathbb{R}^n$ and let $X=(\mathbb{R}^n,\|\cdot\|)$ be a normed space. A subspace $Y\subset X$ is \emph{strongly $\alpha$-Euclidean} if there is a constant $t$ such that…

The goal of this note is to generalize Thurston's Topological Characterization of Rational Functions to the setting when both the covering degree and the set of marked points are infinite. A relevant class of branched coverings are…

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 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 show that it is consistent to have regular closed non-clopen copies of $\mathbb N^*$ within $\mathbb N^*$ and a non-trivial self-map of $\mathbb N^*$ even if all autohomeomorphisms of $\mathbb N^*$ are trivial.

A tie-point of a compact space is analogous to a cut-point: the complement of the point falls apart into two relatively clopen non-compact subsets. Set-theoretically a tie-point of N* is an ultrafilter whose dual maximal ideal can be…

We prove that each non-metrizable sequential rectifiable space $X$ of countable $cs^*$-character contains a clopen rectifiable submetrizable $k_\omega$-subspace $H$ and admits an open disjoint cover by subspaces homeomorphic to clopen…

We study non-linear functionals, including quasi-linear functionals, p-conic quasi-linear functionals, d-functionals, r-functionals, and their relationships to deficient topological measures and topological measures on locally compact…

Klep and Schweighofer asked whether the Nirgendsnegativsemide-finitheitsstellensatz holds for a symmetric noncommutative polynomial whose evaluations at bounded self-adjoint operators on any nontrivial Hilbert space are not negative…

We focus on a sequence of functions $\{f_n\}$, defined on a compact manifold with boundary $S$, converging in the $C^k$ metric to a limit $f$. A common assumption implicitly made in the empirical sciences is that when such functions…

Let M be a complete non-compact connected Riemannian n-dimensional manifold. We first prove that, for any fixed point p in M, the radial Ricci curvature of M at p is bounded from below by the radial curvature function of some non-compact…

We show that if a 1-hyperbolic structurally finite entire function of type $(p,q)$, $p\ge 1$, is linearizable at an irrationally indifferent fixed point, then its multiplier satisfies the Brjuno condition. We also prove the generalized…

Function (linear) spaces on which an arbitrary function operates (i.e. the space is stable w.r.t. the pointwise unary operation defined by the function) were investigated, for continuous real or complex operations, by deLeeuw-Katznelson,…

We show that for every $1<n<\infty$, there exits a Banach space $X_n$ containing proximinal subspaces of codimension $n$ but no proximinal finite codimensional subspaces of higher codimension. Moreover, the set of norm-attaining functionals…

For an open set in a compact smooth oriented Riemannian n-manifold and a positive finite Borel measure with support contained in the closure of the open set, we define an associated Krein-Feller operator on k-forms by assuming the Poincare…

We give two examples of metric measure spaces satisfying the measure contraction property MCP(K,N) but having different topological dimensions at different regions of the space. The first one satisfies MCP(0,3) and contains a subset…

Let S be a generic C-infinity smooth CR manifold in C^n, n > 1, and let M be a generic C-infinity CR submanifold of S X C^m. We prescribe conditions on M so that it is the disjoint union of graphs of CR maps f:S-->C^m. We also consider the…

For a compact space $K$, the Banach space $C(K)$ is said to have the $\ell_1$-Grothendieck property if every weak* convergent sequence $\big\langle\mu_n\colon\ n\in\omega\big\rangle$ of functionals on $C(K)$ such that $\mu_n\in\ell_1(K)$…

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…