On the locally countable subalgebra of C(X) whose local domain is cocountable

R. Mehri, R. Mohamadian
2017 Hacettepe Journal of Mathematics and Statistics  
In this paper, we present a new subring of C(X) that contains the subring Cc(X), the set of all continuous functions with countable image. We observe that Lcc(X) enjoys most of the important properties which are shared by C(X) and Cc(X). It is shown that any hereditary lindelöf scattered space is functionally countable. Spaces X such that Lcc(X) is regular (von Neumann) are characterized and it is shown that ℵ0-selfinjectivity and regularity of Lcc(X) coincide.
doi:10.15672/hjms.2017.435 fatcat:s7elybjgcvdjba67g5uwajocme