Some Conditions on Total Boundness (3,2, ρ)-Symmetric Spaces

In this paper some necessary and sufficient conditions under which (3,2, ρ)-symmetric spaces are totally bounded are given. It will be shown that a (3,2)-
$N$
-symmetrizable topological space (M, τ) is totally bounded (3, 2) -symmetric space if and only if it is a regular second-countable space.