Some results in generalized Serstnev spaces

Abstract

We show that D-compactness in generalized Serstnev spaces implies D-boundedness and as in the classical case, a D-bounded and closed subset of a characteristic generalized Serstnev is not D-compact in general. Finally, in the finite dimensional generalized Serstnev spaces a subset is D-compact if, and only if it is D-bounded and closed.