Search results for "General topology"

showing 10 items of 131 documents

On Certain Metrizable Locally Convex Spaces

1986

Publisher Summary This chapter discusses on certain metrizable locally convex spaces. The linear spaces used are defined over the field IK of real or complex numbers. The word "space" will mean "Hausdorff locally convex space". This chapter presents a proposition which states if U be a neighborhood of the origin in a space E. If A is a barrel in E which is not a neighborhood of the origin and F is a closed subspace of finite codimension in E’ [σ(E’,E)], then U° ∩ F does not contain A° ∩ F. Suppose that U° ∩ F contain A° ∩ F. Then A° ∩ F is equicontinuous hence W is also equicontinuous. Since W° is contained in A, it follows that A is a neighborhood of the origin, a contradiction.

CombinatoricsLocally convex topological vector spaceMetrization theoremConvex setHausdorff spaceMathematics::General TopologyField (mathematics)CodimensionSpace (mathematics)EquicontinuityMathematics
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On closures of discrete sets

2018

The depth of a topological space $X$ ($g(X)$) is defined as the supremum of the cardinalities of closures of discrete subsets of $X$. Solving a problem of Mart\'inez-Ruiz, Ram\'irez-P\'aramo and Romero-Morales, we prove that the cardinal inequality $|X| \leq g(X)^{L(X) \cdot F(X)}$ holds for every Hausdorff space $X$, where $L(X)$ is the Lindel\"of number of $X$ and $F(X)$ is the supremum of the cardinalities of the free sequences in $X$.

CombinatoricsMathematics (miscellaneous)Cardinal invariants Lindelof space Discrete set Elementary submodel CellularityGeneral Topology (math.GN)FOS: MathematicsHausdorff spaceMathematics::General TopologySettore MAT/03 - GeometriaTopological spaceDiscrete setInfimum and supremumMathematics - General TopologyMathematics
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K-theory of function rings

1990

AbstractThe ring R of continuous functions on a compact topological space Xwith values in R or C is considered. It is shown that the algebraic K-theory of such rings with coefficients in ZkZ, k any positive integer, agrees with the topological K-theory of the underlying space X with the same coefficient rings. The proof is based on the result that the map from Rδ (R with discrete topology) to R (R with compact-open topology) induces a natural isomorphism between the homologies with coefficients in ZkZ of the classifying spaces of the respective infinite general linear groups. Some remarks on the situation with X not compact are added.

CombinatoricsRing (mathematics)Algebra and Number TheoryDiscrete spaceGeneral topologyTopological groupTopological spaceSpace (mathematics)K-theoryTopological vector spaceMathematicsJournal of Pure and Applied Algebra
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Common fixed points in cone metric spaces for CJM-pairs

2011

Abstract In this paper we introduce some contractive conditions of Meir–Keeler type for two mappings, called f - M K -pair mappings and f - C J M -pair (from Ciric, Jachymski, and Matkowski) mappings, in the framework of regular cone metric spaces and we prove theorems which guarantee the existence and uniqueness of common fixed points. We give also a fixed point result for a multivalued mapping that satisfies a contractive condition of Meir–Keeler type. These results extend and generalize some recent results from the literature. To conclude the paper, we extend our main result to non-regular cone metric spaces by using the scalarization method of Du.

Cone metric spaces CJM-pairs Common fixed points Common coincidence points.Injective metric spaceMathematical analysisMathematics::General TopologyFixed pointComputer Science ApplicationsIntrinsic metricConvex metric spaceCombinatoricsMetric spaceCone (topology)Settore MAT/05 - Analisi MatematicaModeling and SimulationUniquenessCoincidence pointMathematicsMathematical and Computer Modelling
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The Kuratowski convergence and connected components

2012

International audience; We investigate the Kuratowski convergence of the connected components of the sections of a definable set applying the result obtained to semialgebraic approximation of subanalytic sets. We are led to some considerations concerning the connectedness of the limit set in general. We discuss also the behaviour of the dimension of converging sections and prove some general facts about the Kuratowski convergence in tame geometry.

Connected componentDiscrete mathematicsSocial connectednessApplied Mathematics010102 general mathematicsDimension (graph theory)Mathematics::General Topology16. Peace & justiceKuratowski convergencesubanalytic sets01 natural sciencesKuratowski's theoremKuratowski convergence010101 applied mathematicsDefinable setMathematics::Logictame geometry0101 mathematicsLimit set[MATH]Mathematics [math]Kuratowski closure axiomsAnalysisMathematics
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A non-g-contractible uniformly path connected continuum

1999

Abstract An example of a uniformly path connected, plane continuum P is constructed and proved to admit no continuous surjection onto P homotopic to the constant map. This answers a question of D.P. Bellamy in the negative.

Connected spacePlane (geometry)Continuum (topology)HomotopyMathematics::General TopologyContractible spaceSurjective functionCombinatoricsContinuumUniformly path connected spaceGeometry and TopologyHomotopyg-contractibilityConstant (mathematics)MathematicsTopology and its Applications
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On fuzzification of topological categories

2014

This paper shows that (L,M)-fuzzy topology of U. Hohle, T. Kubiak and A. Sostak is an instance of a general fuzzification procedure for topological categories, which amounts to the construction of a new topological category from a given one. This fuzzification procedure motivates a partial dualization of the machinery of tower extension of topological constructs of D. Zhang, thereby providing the procedure of tower extension of topological categories. With the help of this dualization, we arrive at the meta-mathematical result that the concept of (L,M)-fuzzy topology and the notion of approach space of R. Lowen are ''dual'' to each other.

Connected spaceTopological algebraArtificial IntelligenceLogicMathematics::Category TheoryCategory of topological spacesGeneral topologyTopological spaceTopologyTopological vector spaceHomeomorphismMathematicsTopological categoryFuzzy Sets and Systems
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"Table 6" of "Transverse momentum of J / psi produced in p Cu, p U, O-16 Cu, O-16 U and S-32 U collisions at 200-GeV per nucleon."

1991

CONTINUUM MUONS ORIGINATE MAINLY FROM VECTOR MESON DECAYS, SEMI-LEPTONIC DECAYS OF D DBAR PAIRS AND FROM DRELL-YAN MECHANISM.

Di-Muon ProductionNuclear TheoryHigh Energy Physics::PhenomenologyMathematics::General TopologyMuon productionJ/PsiInclusiveSingle Differential Cross SectionO16 U --> MU- MU+ (NEUTRALS) XNUCLEUS NUCLEUS --> (NEUTRALS) MU+ MU- XHigh Energy Physics::ExperimentDSIG/DPTPsiNuclear ExperimentTransverse Momentum DependenceDrell Yan
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"Table 8" of "Transverse momentum of J / psi produced in p Cu, p U, O-16 Cu, O-16 U and S-32 U collisions at 200-GeV per nucleon."

1991

CONTINUUM MUONS ORIGINATE MAINLY FROM VECTOR MESON DECAYS, SEMI-LEPTONIC DECAYS OF D DBAR PAIRS AND FROM DRELL-YAN MECHANISM.

Di-Muon ProductionNuclear TheoryHigh Energy Physics::PhenomenologyMathematics::General TopologyMuon productionJ/PsiS32 U --> MU- MU+ (NEUTRALS) XInclusiveSingle Differential Cross SectionNUCLEUS NUCLEUS --> (NEUTRALS) MU+ MU- XHigh Energy Physics::ExperimentDSIG/DPTPsiNuclear ExperimentTransverse Momentum DependenceDrell Yan
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"Table 4" of "Transverse momentum of J / psi produced in p Cu, p U, O-16 Cu, O-16 U and S-32 U collisions at 200-GeV per nucleon."

1991

CONTINUUM MUONS ORIGINATE MAINLY FROM VECTOR MESON DECAYS, SEMI-LEPTONIC DECAYS OF D DBAR PAIRS AND FROM DRELL-YAN MECHANISM.

Di-Muon ProductionNuclear TheoryHigh Energy Physics::PhenomenologyMathematics::General TopologyO16 CU --> MU- MU+ (NEUTRALS) XMuon productionJ/PsiInclusiveSingle Differential Cross SectionNUCLEUS NUCLEUS --> (NEUTRALS) MU+ MU- XHigh Energy Physics::ExperimentDSIG/DPTPsiNuclear ExperimentTransverse Momentum DependenceDrell Yan
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