Topological characterization of equivalent uniformities in topological groups
Salvador Hernández
We characterize the topological groups with equivalent left and right
uniform structures (SIN groups) by means of their uniformly discrete
subsets.
As a consequence, it follows that a \omega-bounded non-Archimedean group
G is SIN if and only if every left uniformly continuous real-valued
function on G is right uniformly continuous.
And, in general, a topological group is SIN if and only if every set of left
(right) equiuniformly real-valued functions on G is right
(left) equiuniformly continuous.
