1. Norm continuity of pointwise quasi-continuous mappings
- Creator:
- Mirmostafaee, Alireza Kamel
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- function space, weak continuity, generalized continuity, quasi-continuous function, and pointwise topology
- Language:
- English
- Description:
- Let X be a Baire space, Y be a compact Hausdorff space and ϕ: X → Cp(Y ) be a quasi-continuous mapping. For a proximal subset H of Y × Y we will use topological games G1(H) and G2(H) on Y × Y between two players to prove that if the first player has a winning strategy in these games, then ϕ is norm continuous on a dense Gδ subset of X. It follows that if Y is Valdivia compact, each quasi-continuous mapping from a Baire space X to Cp(Y ) is norm continuous on a dense Gδ subset of X.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public