Related papers: A classification of Tsirelson type spaces
Let 0-CR denote the class of all metric compacta X such that the set of maps $f:X\to X$ with 0-dimensional sets CR(f) of chain recurrent points is a dense $G_\delta$-subset of the mapping space C(X,X) (with the uniform convergence). We…
An orthogonality space is a set together with a symmetric and irreflexive binary relation. Any linear space equipped with a reflexive and anisotropic inner product provides an example: the set of one-dimensional subspaces together with the…
We use a coarse version of the fundamental group first introduced by Barcelo, Kramer, Laubenbacher and Weaver to show that box spaces of finitely presented groups detect the normal subgroups used to construct the box space, up to…
In the absence of the axiom of choice, new results concerning sequential, Fr\'echet-Urysohn, $k$-spaces, very $k$-spaces, Loeb and Cantor completely metrizable spaces are shown. New choice principles are introduced. Among many other…
We define a diffeology on the Milnor classifying space of a diffeological group $G$, constructed in a similar fashion to the topological version using an infinite join. Besides obtaining the expected classification theorem for smooth…
Let $G$ be a finitely generated Kleinian group and let $\Delta$ be an invariant collection of components in its region of discontinuity. The Teichm\"uller space $T(\Delta,G)$ supported in $\Delta$, is the space of equivalence classes of…
Torelli space (in genus g) is the moduli space of compact Riemann surfaces of genus g together with a symplectic basis of their first homology group. It is the quotient of the genus g Teichmuller space by the Torelli group T_g and is a…
We construct a trigonometric series converging to zero everywhere on a subsequence, with coefficients tending to zero. We show that any such series must satisfy that the subsequence is very sparse, and that the support of the related…
A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…
In this paper, we study tensor (or monoidal) categories of finite rank over an algebraically closed field $\mathbb F$. Given a tensor category $\mathcal{C}$, we have two structure invariants of $\mathcal{C}$: the Green ring (or the…
Let $C(F)$ be a matrix Cayley-Dickson algebra over field $F$. By $M_0(F)$ we denote the loop containing of all elements of algebra $C(F)$ with norm 1. It is shown in this paper that with precision till isomorphism the loops $M_0(F)/<-1>$…
We show that square(theta) implies that there is a first countable <theta-collectionwise Hausdorff space that is not weakly theta-collectionwise Hausdorff. We also show that in the model obtained by Levy collapsing a weakly compact…
A direction in a Type I space $X=\cup_{\alpha<\omega_1}X_\alpha$ is a closed and unbounded subset $D$ of $X$ such that given any continuous $f:X\to\mathbb{L}_{\ge 0}$ (the closed long ray), if $f$ is unbounded on $D$ then $f$ is unbounded…
We describe and classify countable Boolean rings (which may or may not have a multiplicative identity) with finitely many distinguished ideals whose elementary theory is countably categorical. This extends the description by Macintyre and…
We examine locally compact normal spaces in models of form PFA(S)[S], in particular characterizing paracompact, countably tight ones as those which include no perfect pre-image of omega_1 and in which all separable closed subspaces are…
In this paper, plane polynomial systems having a singular point attracting all orbits in positive time are classified up to topological equivalence. This is done by assigning a combinatorial invariant to the system (a so-called "feasible…
Starting from compact symmetric spaces of inner type, we provide infinite families of compact homogeneous spaces carrying invariant non-flat Bismut connections with vanishing Ricci tensor. These examples turn out to be generalized symmetric…
In this paper we complete a chain of explicit Quillen equivalences between the model category for $\Theta_{n+1}$-spaces and the model category of small categories enriched in $\Theta_n$-spaces. The Quillen equivalences given here connect…
We investigate $\mathcal F$-Borel topological spaces. We focus on finding out how a~complexity of a~space depends on where the~space is embedded. Of a~particular interest is the~problem of determining whether a~complexity of given space $X$…
In this article, we mainly study certain families of continuous retractions ($r$-skeletons) having certain rich properties. By using monotonically retractable spaces we solve a question posed by R. Z. Buzyakova in \cite{buz} concerning the…