Cellular space

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A Hausdorff space provided with the structure of a CW-complex. For example, every simplicial space is a cellular space. Conversely, there exists for any cellular space a simplicial space of the same dimension that is homotopically equivalent to it.


[1] V.A. Rokhlin, D.B. Fuks, "Beginner's course in topology. Geometric chapters", Springer (1984) (Translated from Russian)
[a1] K. Jänich, "Topology", Springer (1984) pp. Chapt. VII (Translated from German)
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Cellular space. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by S.N. Malygin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article