Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userOn dimension and weight of a local contact algebra
336
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
As proved by Dimov [Acta Math. Hungarica, 129 (2010), 314--349], there exists a duality L between the category HLC of locally compact Hausdorff spaces and continuous maps, and the category DHLC of complete local contact algebras and appropriate morphisms between them. In this paper, we introduce the notions of weight and of dimension of a local contact algebra, and we prove that if X is a locally compact Hausdorff space then w(X)=w(L(X)), and if, in addition, X is normal, then dim(X)=dim(L(X)).
rate research
Read More
The result of Boyce and Huneke gives rise to a 1-dimensional continuum, which is the intersection of a descending family of disks, that admits two commuting homeomorphisms without a common fixed point.
This paper is a contribution to understanding what properties should a topological algebra on a Stone space satisfy to be profinite. We reformulate and simplify proofs for some known properties using syntactic congruences. We also clarify the role of various alternative ways of describing syntactic congruences, namely by finite sets of terms and by compact sets of continuous self mappings of the algebra.
Hindmans celebrated Finite Sums Theorem, and its high-dimensional version due to Milliken and Taylor, are extended from covers of countable sets to covers of arbitrary topological spaces with Mengers classic covering property. The methods include, in addition to Hurewiczs game theoretic characterization of Mengers property, extensions of the classic idempotent theory in the Stone--Czech compactification of semigroups, and of the more recent theory of selection principles. This provides stro
Given a countable group $X$ we study the algebraic structure of its superextension $lambda(X)$. This is a right-topological semigroup consisting of all maximal linked systems on $X$ endowed with the operation $$mathcal Acircmathcal B={Csubset X:{xin X:x^{-1}Cinmathcal B}inmathcal A}$$ that extends the group operation of $X$. We show that the subsemigroup $lambda^circ(X)$ of free maximal linked systems contains an open dense subset of right cancelable elements. Also we prove that the topological center of $lambda(X)$ coincides with the subsemigroup $lambda^bullet(X)$ of all maximal linked systems with finite support. This result is applied to show that the algebraic center of $lambda(X)$ coincides with the algebraic center of $X$ provided $X$ is countably infinite. On the other hand, for finite groups $X$ of order $3le|X|le5$ the algebraic center of $lambda(X)$ is strictly larger than the algebraic center of $X$.
We prove that the existence of a Borel lower density operator (a Borel lifting) with respect to the $sigma$-ideal of countable sets, for an uncountable Polish space, is equivalent to the Continuum Hypothesis.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
