**MSC:**- 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, etc.)
- 54B30 Categorical methods, See also {18B30}
- 54E05 Proximity structures and generalizations
- 54E15 Uniform structures and generalizations
- 54E17 Nearness spaces

$Conv_S$, the category of symmetric convergence spaces, and $Chy$,

the category of Cauchy spaces, can be fully embedded into the

Kat\v etov's category $Fil$ of filter-merotopic spaces [9]. $Fil$

is a bicoreflective subcategory of $Mer$, the category of

merotopic spaces, which is closely related to the concept of

nearness introduced by Herrlich [8] who basically uses notions of

set systems which are near. Kat\v etov proved that $Fil$ is

cartesian closed and that the corresponding function space

structure is the one of continuous convergence.