Results 1 to 10 of about 170 (133)

The Frame of Nuclei on an Alexandroff Space [PDF]

Order, 2020
Let $\mathcal{O}S$ be the frame of open sets of a topological space $S$, and let $N(\mathcal{O}S)$ be the frame of nuclei of $\mathcal{O}S$. For an Alexandroff space $S$, we prove that $N(\mathcal{O}S)$ is spatial iff the infinite binary tree $\mathscr T_2$ does not embed isomorphically into $(S, \le)$, where $\le$ is the specialization preorder of $S$.
G Bezhanishvili, P J Morandi, Bezhanishvili G   +2 more
exaly   +3 more sources

PRE-ALEXANDROFF SPACE

مجلة علوم ذي قار, 2019
In this paper we introduce a new definition of the topological space weaker of Alexandroff space, namely pre-Alexandroff space. These spaces are which arbitrary intersection of an open set is a pre-open set.
Ayed .E. Hashoosh Al-Badry
doaj   +3 more sources

On Homotopy Types of Alexandroff Spaces [PDF]

Order, 2009
We generalise some results of R. E. Stong concerning finite spaces to wider subclasses of Alexandroff spaces. These include theorems on function spaces, cores and homotopy type. In particular, we characterize pairs of spaces X,Y such that the compact-open topology on C(X,Y) is Alexandroff, introduce the classes of finite-paths and bounded-paths spaces ...
exaly   +4 more sources

The Avoidance Spectrum of Alexandroff Spaces

Universitas Scientiarum
In this paper we prove that every T0 Alexandroff topological space (𝑋, 𝜏) is homeomorphic to the avoidance of a subspace of (Spec(Λ), 𝜏𝑍), where Spec(Λ) denotes the prime spectrum of a semi-ring Λ induced by 𝜏, and 𝜏𝑍 is the Zariski topology.
Jorge Vielma, Luis Mejias
doaj   +2 more sources

The Alexandroff-Urysohn Square and the Fixed Point Property

Fixed Point Theory and Applications, 2009
Every continuous function of the Alexandroff-Urysohn Square into itself has a fixed point. This follows from G. S. Young's general theorem (1946) that establishes the fixed-point property for every arcwise connected Hausdorff space in which each ...
Hagopian CL, Marsh MM, Foregger TH
doaj   +3 more sources

Results about the Alexandroff duplicate space

Applied General Topology, 2016
In this paper, we present some new results about the  Alexandroff Duplicate Space. We prove that if a space X has the property P, then its Alexandroff Duplicate space A(X) may not have P, where P is one of the following properties: extremally ...
Khulod Almontashery, Lutfi Kalantan
doaj   +4 more sources

Fenestrations induced by perfect tilings

Applied General Topology, 2002
In this paper we study those regular fenestrations (as defined by Kronheimer in [3]) that are obtained from a tiling of a topological space. Under weak conditions we obtain that the canonical grid is also the minimal grid associated to each tiling and we
F.G. Arenas, M.L. Puertas
doaj   +3 more sources

Generalized Alexandroff Duplicates and CD 0(K) spaces

Central European Journal of Mathematics, 2006
Abstract We define and investigateCD Σ,Γ(K, E)-type spaces, which generalizeCD 0-type Banach lattices introduced in [1]. We state that the space CD Σ,Γ(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff Duplicate of K. As a corollary we obtain the main result of [6, 8].
Faruk Polat
exaly   +5 more sources

Disconnection in the Alexandroff duplicate

Applied General Topology, 2021
It was demonstrated in [2] that the Alexandroff duplicate of the Čech-Stone compactification of the naturals is not extremally disconnected. The question was raised as to whether the Alexandroff duplicate of a non-discrete extremally disconnected space ...
Papiya Bhattacharjee, Michelle L. Knox, Warren Wm. McGovern   +2 more
doaj   +1 more source

Alexandroff duplicate and βκ

Applied General Topology, 2022
We discuss spaces and the Alexandroff duplicates of those spaces that admit a Č-S embedding into the Čech-Stone compactification of a discrete space.
Andrzej A Szymanski
doaj   +1 more source