Back Categoría de espacios topológicos Spanish Catégorie des espaces topologiques French Kategori ruang topologi ID 位相空間の圏 Japanese 위상 공간의 범주 Korean Categorie van topologische ruimten Dutch Kategoria przestrzeni topologicznych Polish Категория топологических пространств Russian 拓撲空間範疇 Chinese
In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps. This is a category because the composition of two continuous maps is again continuous, and the identity function is continuous. The study of Top and of properties of topological spaces using the techniques of category theory is known as categorical topology.
N.B. Some authors use the name Top for the categories with topological manifolds, with compactly generated spaces as objects and continuous maps as morphisms or with the category of compactly generated weak Hausdorff spaces.