Catalogue Search | MBRL
Are you sure you want to remove the book from the shelf?
{{itemTitle}}
1,940
result(s) for
"Compact space"
Sort by:
Deriving Dualities in Pointfree Topology from Priestley Duality
There are several prominent duality results in pointfree topology. Hofmann–Lawson duality establishes that the category of continuous frames is dually equivalent to the category of locally compact sober spaces. This restricts to a dual equivalence between the categories of stably continuous frames and stably locally compact spaces, which further restricts to Isbell duality between the categories of compact regular frames and compact Hausdorff spaces. We show how to derive these dualities from Priestley duality for distributive lattices, thus shedding new light on these classic results.
Journal Article
On r-Compactness in Topological and Bitopological Spaces
This paper defines the so-called pairwise r-compactness in topological and bitopological spaces. In particular, several inferred properties of the r-compact spaces and their connections with other topological and bitopological spaces are studied theoretically. As a result, several novel theorems of the r-compact space are generalized on the pairwise r-compact space. The results established in this research paper are new in the field of topology.
Journal Article
Almost compactness in neutrosophic topological spaces
The aim of this write-up is to investigate some covering properties in neutrosophic topological spaces. We define proximate cover, almost compactness, almost countable compactness and almost Lindelöfness in connection with neutrosophic topological spaces and study some properties entangled with them.
Journal Article
A Novel Class of Separation Axioms, Compactness, and Continuity via C-Open Sets
In this paper, we originate a new class of open sets, namely C-open sets, and we review its important properties. Then, some separation axioms of C-open sets are introduced and investigated. In addition, we define the so-called C-compact and C′-compact spaces via C-open sets, and the theorems based on them are discussed with counterexamples. Moreover, we entitle the C-continuous and C′-continuous functions by applying C-open sets. In particular, several inferred properties of them and their connection with the other topological spaces are studied theoretically. Many examples are given to explain the concepts lucidly. The results established in this research paper are new in the field of topology.
Journal Article
Commutative Topological Semigroups Embedded into Topological Abelian Groups
In this paper, we give conditions under which a commutative topological semigroup can be embedded algebraically and topologically into a compact topological Abelian group. We prove that every feebly compact regular first countable cancellative commutative topological semigroup with open shifts is a topological group, as well as every connected locally compact Hausdorff cancellative commutative topological monoid with open shifts. Finally, we use these results to give sufficient conditions on a commutative topological semigroup that guarantee it to have countable cellularity.
Journal Article
Maximal Ideals in Rings of Real Measurable Functions
Let M(X) be the ring of all real measurable functions on a measurable space (X, A). In this article, we show that every ideal of M(X) is a Z°-ideal. Also, we give several characterizations of maximal ideals of M(X), mostly in terms of certain lattice-theoretic properties of A. The notion of T-measurable space is introduced. Next, we show that for every measurable space (X.A) there exists a T-measurable space (Y, A’) such that M(X) ≅ M(Y) as rings. The notion of compact measurable space is introduced. Next, we prove that if (X, A) and (Y, A’) are two compact T-measurable spaces, then X ≅ Y as measurable spaces if and only if M(X) ≅ M(Y) as rings.
Journal Article
One-Point λ-Compactification via Grills
A space Y is called an extension of a space X if Y contains X as a dense subspace. An extension Y of X is called a one-point extension of X if Y\\X is a singleton. In present paper, we extend the well-known and important fact \"any locally compact Hausdorff non-compact space X has a one-point compact Hausdorif extension\", which was proved by Alexandroff, to more general topological space.
Journal Article
Maximal pseudocompact spaces and the Preiss-Simon property
We study maximal pseudocompact spaces calling them also MP-spaces. We show that the product of a maximal pseudocompact space and a countable compact space is maximal pseudocompact. If X is hereditarily maximal pseudocompact then X × Y is hereditarily maximal pseudocompact for any first countable compact space Y. It turns out that hereditary maximal pseudocompactness coincides with the Preiss-Simon property in countably compact spaces. In compact spaces, hereditary MP-property is invariant under continuous images while this is not true for the class of countably compact spaces. We prove that every Fréchet-Urysohn compact space is homeomorphic to a retract of a compact MP-space. We also give a ZFC example of a Fréchet-Urysohn compact space which is not maximal pseudocompact. Therefore maximal pseudocompactness is not preserved by continuous images in the class of compact spaces.
Journal Article