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New approach for closure spaces by relations.

Allam, A.A., Bakeir, M.Y., Abo-Tabl, E.A. (2006)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

Non-constant continuous mappings of metric or compact Hausdorff spaces

Věra Trnková (1972)

Commentationes Mathematicae Universitatis Carolinae

Norm continuity of pointwise quasi-continuous mappings

Alireza Kamel Mirmostafaee (2018)

Mathematica Bohemica

Let $X$ be a Baire space, $Y$ be a compact Hausdorff space and $ϕ : X \to C_{p} (Y)$ be a quasi-continuous mapping. For a proximal subset $H$ of $Y \times Y$ we will use topological games $𝒢_{1} (H)$ and $𝒢_{2} (H)$ on $Y \times Y$ 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 $G_{δ}$ subset of $X$ . It follows that if $Y$ is Valdivia compact, each quasi-continuous mapping from a Baire space $X$ to $C_{p} (Y)$ is norm continuous on a dense $G_{δ}$ subset of $X$ .