Some properties of regular topology on C(X, Y )

The recently introduced regular topology for the function space C(X, Y ) has been explored up to some metrizability and various countability and completeness properties. The main aim of this paper is to explore the regular topology on the function space C(X, Y ) in which we study submetrizability and extend various properties equivalent to the metrizability of the space Cr(X, Y ). We also study number of maps corresponding to the space Cr(X, Y ) and prove that the regular topology on the space C(X, Y ) is strong when X is taken discrete. Furthermore, we study various separation axioms on the space Cr(X, Y ), where we prove that the function space Cr(X) is normal by taking X to be countable, compactly generated compact space and prove certain equivalent conditions to various separation axioms on the space Cr(X, Y ).