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. 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 category with topological manifolds as objects and continuous maps as morphisms.
Read more about Category Of Topological Spaces: As A Concrete Category, Limits and Colimits, Other Properties, Relationships To Other Categories
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