Quotients of Raikov-complete topological groups

A topological group X is called Raikov-complete if the two sides uniformity on X, that is the supremum of the left uniformity and the right uniformity on X, is complete.It will be proved that the quotient of an inframetrizable Raikov-complete topological group X with a neutral subgroup G is complete.(If G is normal (and therefore neutral), the completeness of is equivalent to the Raikov-completeness of the quotient group ).The proof consist in an intricate lifting of -Cauchy filters. Where it is possible, the results on topological groups will be derived from results on uniform spaces