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als tussen twee topologische ruimten een homeomorfisme bestaat, worden ze als topologisch gelijkwaardig beschouwd.
two spaces with a homeomorphism between them are called homeomorphic, and from a topological viewpoint they are the same.
dergelijke constructies heten meestal compactificatie, omdat de nieuwe, eenvoudigere ruimte topologisch compact is.
thus the circle is the one-point compactification of the real line, and the sphere is the one-point compactification of the plane.
== definitie ==een "kolmogorov-ruimte" is een topologische ruimte waarin elk paar verschillende punten topologisch onderscheidbaar is.
== definition ==a t0 space is a topological space in which every pair of distinct points is topologically distinguishable.