Results 31 to 40 of about 361 (62)
Applications of δ‐Open Sets via Separation Axioms, Covering Properties, and Rough Set Models
Journal of Mathematics, Volume 2025, Issue 1, 2025.In this article, we make use of δ‐open sets to establish some topological concepts related to separation axioms and covering properties and to propose novel topological rough set models. We first demonstrate that the classes of regular‐open and δ‐open subsets of a finite topological space are equivalent when this space has the property of ∂(A)∩∂(B)⊆∂(A
Tareq M. Al-Shami +2 more
wiley +1 more source
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 3, Page 507-512, 1990., 1989 An ideal on a set X is a nonempty collection of subsets of X closed under the operations of subset (heredity) and finite unions (additivity). Given a topological space (X, τ) an ideal ℐ on X and A⊆X, ψ(A) is defined as ⋃{U ∈ τ : U − A ∈ ℐ}. A topology, denoted τ*, finer than τ is generated by the basis {U − I : U ∈ τ, I ∈ ℐ}, and a topology, denoted 〈ψ(
T. R. Hamlett, David Rose
wiley +1 more source
A topological property of β(N)
International Journal of Mathematics and Mathematical Sciences, Volume 3, Issue 4, Page 713-717, 1980., 1980 In this paper we prove that the Stone‐Cech‐compactification of the natural numbers does not admit a countable infinite decomposition into subsets homeomorphic to each other and to the said compactification.
Anastase Nakassis
wiley +1 more source
, 2009 In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup $H(e)$ in $S$ is a (closed) topological subgroup in $S$; (ii) the Clifford part $H(S)$(i.e.
A. B. Paalman-de-Miranda +17 more
core +1 more source
Large separated sets of unit vectors in Banach spaces of continuous functions
, 2019 The paper concerns the problem whether a nonseparable $\C(K)$ space must contain a set of unit vectors whose cardinality equals to the density of $\C(K)$ such that the distances between every two distinct vectors are always greater than one.
Cúth, Marek +2 more
core +1 more source
A decomposition theorem for compact groups with application to supercompactness
, 2010 We show that every compact connected group is the limit of a continuous inverse sequence, in the category of compact groups, where each successor bonding map is either an epimorphism with finite kernel or the projection from a product by a simple compact
C.F. Mills +7 more
core +1 more source
Set-theoretic problems concerning Lindelof spaces [PDF]
, 2010 I survey problems concerning Lindelof spaces which have partial set- theoretic ...
Tall, Franklin D.
core
The basis problem for subspaces of monotonically normal compacta
, 2016 We prove, assuming Souslin's Hypothesis, that each uncountable subspace of each zero-dimensional monotonically normal compact space contains an uncountable subset of the real line with either the metric, the Sorgenfrey, or the discrete topology.Comment ...
Ahmad Farhat +23 more
core +1 more source
Base-free Formulas in the Lattice-theoretic Study of Compacta [PDF]
, 2011 The languages of finitary and infinitary logic over the alphabet of bounded lattices have proven to be of considerable use in the study of compacta. Significant among the sentences of these languages are the ones that are base free, those whose truth is ...
Bankston, Paul
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Topological partition relations to the form omega^*-> (Y)^1_2
, 1993 Theorem: The topological partition relation omega^{*}-> (Y)^{1}_{2} (a) fails for every space Y with |Y| >= 2^c ; (b) holds for Y discrete if and only if |Y|
Comfort W. W. +12 more
core +1 more source