Dieter Leseberg
A note on antitonic convergence
The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 54, 39-50 (2000)

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

Abstract: In the joint paper [2], Bentley, Herrlich and Lowen-Colebunders noted that
$Conv_S$, 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.
Keywords: Convergence in general topology (sequences, filters, limits, convergence spaces, etc.), Categorical methods, Proximity structures and generalizations, Uniform structures and generalizations, Nearness spaces