Topological and geometrical properties of spaces with symmetric and nonsymmetric f-quasimetrics

The properties of spaces equipped with a topology defined by a distance function are studied. The considered distance function is not necessarily symmetric but satisfies the so-called f-triangle inequality, which is a weakened version of the usual triangle inequality. Sufficient conditions for metrizability of such spaces are proposed. A construction of a quasimetric topologically equivalent to a given f-quasimetric is proposed.