Properties of the weak and weak topologies of function spaces

J. C. Ferrando, S. Gabriyelyan

Research output: Contribution to journalArticlepeer-review


Let X be a Tychonoff space, and let S be a directed family of functionally bounded subsets of X containing all finite subsets of X. Denote by CTS(X) the space of all continuous functions on X endowed with the topology of uniform convergence on the sets of the family S. We characterize X for which the space CTS(X) endowed with the weak topology satisfies numerous weak barrelledness conditions or (DF)-type properties, or it has a locally convex property stronger than the property of being a Mackey space. It is shown that the dual space of CTS(X) is weak sequentially Ascoli iff X is finite. We prove also that if CTS(X) is an ℓ-quasibarrelled space, then the strong dual of CTS(X) is a weakly sequentially Ascoli space iff X is finite.

Original languageAmerican English
Article number20
JournalRevista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
Issue number1
StatePublished - 1 Jan 2023


  • Baire space
  • Feral
  • Function space
  • Sequentially Ascoli space
  • Weak barrelledness condition
  • Weak topology
  • Čech-complete space

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology
  • Computational Mathematics
  • Applied Mathematics


Dive into the research topics of 'Properties of the weak and weak topologies of function spaces'. Together they form a unique fingerprint.

Cite this