A special kind of topology on $C(X)$ lying between the point-open topology and the topology of uniform convergence

Soumajit Dey, Sudip Kumar Acharyya, and Dhananjoy Mandal

Let $X$ be a topological space. For each transfinite cardinal number ${\aleph }_{\alpha }$, we define a topology $C_{{\aleph }_{\alpha }}(X)$ on the ring $C(X)$. With ${\aleph }_{\alpha }={\aleph }_0$, $C_{\aleph_α}(…