Results 61 to 70 of about 365 (176)

The Mumford conjecture (after Bianchi)

Journal of Topology, Volume 18, Issue 1, March 2025.
Abstract We give a self‐contained and streamlined rendition of Andrea Bianchi's recent proof of the Mumford conjecture using moduli spaces of branched covers.
Ronno Das, Dan Petersen
wiley   +1 more source

A Characterization of Affine Primal Topological Spaces Induced by Nilpotent Matrices

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
In this article, we prove that an n × n matrix A is nilpotent if and only if there exists an affine primal topology τ for Rn such that the space Rn,τ is both compact and connected. For τ being an affine primal topology, we mean that τ=U⊂Rn:f−1U⊂U, where f:Rn⟶Rn is a map defined by f(x) = Ax + p, with p∈Rn.
Ebner Pineda, Luis Mejías, Jorge Vielma, Ahmed I. Zayed   +3 more
wiley   +1 more source

Parabolic isometries of the fine curve graph of the torus

Proceedings of the London Mathematical Society, Volume 129, Issue 2, August 2024.
Abstract In this article, we finish the classification of actions of torus homeomorphisms on the fine curve graph initiated by Bowden, Hensel, Mann, Militon, and Webb. This is made by proving that if f∈Homeo(T2)$f \in \mathrm{Homeo}(\mathbb {T}^2)$, then f$f$ acts elliptically on C†(T2)$\mathcal {C}^{\dagger }(\mathbb {T}^2)$ if and only if f$f$ has ...
Pierre‐Antoine Guihéneuf, Emmanuel Militon   +1 more
wiley   +1 more source

Homogeneous ANR-spaces and Alexandroff manifolds

Topology and its Applications, 2014
10 ...
openaire   +2 more sources

On the metric reflection of a pseudometric space in ZF [PDF]

, 2015
summary:We show: (i) The countable axiom of choice $\mathbf{CAC}$ is equivalent to each one of the statements: (a) a pseudometric space is sequentially compact iff its metric reflection is sequentially compact, (b) a pseudometric space is complete iff ...
Keremedis, Kyriakos, Herrlich, Horst
core   +1 more source

On local semirings induced by topologies: An algebraic approach to the Collatz conjecture

Applied General Topology
We present an algebraic approach to the Collatz conjecture by studying the topology τf  on ℕ induced by the Collatz function f, where the open sets θ ⊂ ℕ satisfy f-1 ( θ ) ⊂ θ .
Angel Guale, Jorge Vielma
doaj   +1 more source

rw*-closed sets in Alexandroff Spaces

Journal of Physics: Conference Series, 2020
Abstract This paper explained and defined the notion of regular weakly-star closed (briefly known as rw*-closed) sets in alexandroff spaces in which every point has a minimal neighbourhood. We discuss the characterizations and study their properties based on set theory along with the notion of rw*-open sets.
N Bhardwaj, P Sharma
openaire   +1 more source

Generalized Alexandroff–Urysohn squares and a characterization of the fixed point property

, 2010
Given a Hausdorff continuum X, we introduce a topology on X×X that yields a Hausdorff continuum. We call the resulting space the Alexandroff–Urysohn square of X and prove that X has the fixed point property if and only if the Alexandroff–Urysohn square ...
Hagopian, C.L., Marsh, M.M.
core   +1 more source

On locally compact shift continuous topologies on the semigroup $\boldsymbol{B}_{[0,\infty)}$ with an adjoined compact ideal

Математичні Студії
Let $[0,\infty)$ be the set of all non-negative real numbers. The set $\boldsymbol{B}_{[0,\infty)}=[0,\infty)\times [0,\infty)$ with the following binary operation $(a,b)(c,d)=(a+c-\min\{b,c\},b+d-\min\{b,c\})$ is a bisimple inverse semigroup.
O. V. Gutik, M. B. Khylynskyi
doaj   +1 more source

ALEXANDROFF SPACES

, 1999
In this paper we mean by an Alexandroff space a topological space such that every point has a minimal neighborhood. We do not assume that the space is T0. There spaces were first introduced by P.
F. G. Arenas
core