λ-Topologies on Function Spaces

This paper is devoted to the spaces C _λ(X) of all continuous real-valued functions on X endowed with arbitrary λ-topologies. This is a fairly complete survey of the results obtained by the author in the following domains of the theory of λ-topologies: cardinal functions; locally convex properties; weak and strong topologies; dual spaces; lattices of λ-topologies; completeness. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 2, pp. 3–56, 2003.