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Category of topological spaces
In
mathematics
, the
category of topological spaces
, often denoted
Top
, is the
category
whose
object
s are
topological spaces
and whose
morphisms
are
continuous maps
or some other variant; for example, objects are often assumed to be
compactly generated
. 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
.
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