A quasitopos containing CONV and MET as full subcategories

We show that convergence spaces with continuous maps and metric spaces with contractions, can be viewed as entities of the same kind. Both can be characterized by a “limit function” λ which with each filter ℱ associates a map λℱ from the underlying set to the extended positive real line. Continuous maps and contractions can both be characterized as limit function preserving maps.

# Mathematics # limit # distance # convergence space # metric space # approach space # cartesian closed # hereditary.

E. Lowen, R. Lowen (1988). "A quasitopos containing CONV and MET as full subcategories". International Journal of Mathematics and Mathematical Sciences. https://doi.org/10.1155/s016117128800050x