6533b838fe1ef96bd12a48d6
RESEARCH PRODUCT
Group topologies coarser than the Isbell topology
Francis JordanSzymon DoleckiFrédéric Mynardsubject
54C35 54C40 54A10Function spaceGroup (mathematics)HyperspaceGeneral Topology (math.GN)Isbell topologyInfraconsonanceTopological spaceFunction spaceTopologyTopological vector spaceTopological groupFunctional Analysis (math.FA)Mathematics - Functional AnalysisHyperspaceFOS: MathematicsTopological groupGeometry and TopologyConsonanceTopology (chemistry)Vector spaceMathematicsMathematics - General Topologydescription
Abstract The Isbell, compact-open and point-open topologies on the set C ( X , R ) of continuous real-valued maps can be represented as the dual topologies with respect to some collections α ( X ) of compact families of open subsets of a topological space X . Those α ( X ) for which addition is jointly continuous at the zero function in C α ( X , R ) are characterized, and sufficient conditions for translations to be continuous are found. As a result, collections α ( X ) for which C α ( X , R ) is a topological vector space are defined canonically. The Isbell topology coincides with this vector space topology if and only if X is infraconsonant. Examples based on measure theoretic methods, that C α ( X , R ) can be strictly finer than the compact-open topology, are given. To our knowledge, this is the first example of a splitting group topology strictly finer than the compact-open topology.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-09-01 |