Topologies on the space of continuous functions

DOI10.1016/S0166-8641(97)00114-4zbMath0940.54023MaRDI QIDQ1295271

V. Pereyra

Publication date: 11 October 1999

Published in: Topology and its Applications (Search for Journal in Brave)

zbMATH Keywords

fine topologygraph topologycountably compactfunction spacetopology of uniform convergencepseudocompactcardinal functionscountably paracompactopen-cover topologycoincidence of topologiesequinormalKrikorian topologym-topology

Mathematics Subject Classification ID

Continuous maps (54C05) Function spaces in general topology (54C35) Metric spaces, metrizability (54E35) Uniform structures and generalizations (54E15) Proximity structures and generalizations (54E05)

Related Items (30)

Topology of uniform convergence and \(m\)-topology on \(C(X)\) ⋮ Closed ideals in the functionally countable subalgebra of C(X) ⋮ The largest topological ring of functions endowed with the m-topology ⋮ Uniform boundedness in function spaces ⋮ Cauchy convergence topologies on the space of continuous functions ⋮ Cardinal functions, bornologies and strong Whitney convergence ⋮ Lipschitz extensions and approximations ⋮ Clopen linear subspaces and connectedness in function spaces ⋮ Topologicality of the Whitney topology on function spaces in the \(\omega_\mu\)-metric framework ⋮ Topologies of uniform convergence. The property in the sense of Arens-Dugundji and the sequential property ⋮ Graphical convergence of continuous functions ⋮ ON THE m_c-TOPOLOGY ON THE FUNCTIONALLY COUNTABLE SUBALGEBRA OF C(X) ⋮ Topological properties of the multifunction space L(X) of cusco maps ⋮ Some properties of set-open topologies ⋮ Strong Whitney and strong uniform convergences on a bornology ⋮ A generalization of the m-topology on C(X) finer than the m-topology ⋮ Compactness, connectedness and countability properties of \(C(X)\) with the \(r\)-topology ⋮ Compactness in the fine and related topologies ⋮ \(C(X)\) related to its topological homeomorphism group ⋮ Selections and approximations in finite-dimensional spaces ⋮ The \(m\)-topology on \(C_{m}(x)\) revisited ⋮ Function spaces and product topologies on powers of spaces ⋮ Connectedness and compactness in \(C(X)\) with the \(m\)-topology and generalized \(m\)-topology ⋮ Boundedness properties in function spaces ⋮ Unnamed Item ⋮ On Whitney Convergence ⋮ A study concerning splitting and jointly continuous topologies onC(Y,Z) ⋮ Unnamed Item ⋮ Connectedness of ordered rings of fractions of C(X) with the m-topology ⋮ m-TOPOLOGY ON THE RING OF REAL-MEASURABLE FUNCTIONS

Cites Work

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• Compactness in the fine topology
• Completeness properties of function spaces
• Fine topology on function spaces
• Stone-Čech compactification of a product
• Function space topologies
• Differential Topology
• Cover-close topologies for function spaces
• Graph Topology for Function Spaces
• Semimetrizable and stratifiable spaces
• Rings of Real-Valued Continuous Functions. I

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