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"...a remarkable result of this first period [1930] is his [[topological embedding]] of [[separable space|separable]] [[metric spaces]] into [[compact spaces]] of the same ([[finite set|finite]]) [[dimension]].*"
In the field of general topology his contributions are centred on [[dimension theory]]. He wrote an important text with [[Henry Wallman]], ''[[Dimension Theory]]'', published in 1941.<ref>{{cite journal|author=Smith, P. A.|authorlink=Paul A. Smith|title=Review: ''Dimension Theory'', by W. Hurewicz and H. Wallman|journal=Bull. Amer. Math. Soc.|year=1942|volume=48|issue=9, Part 1|pages=641–642|url=http://www.ams.org/journals/bull/1942-48-09/S0002-9904-1942-07723-8/|doi=10.1090/S0002-9904-1942-07723-8}}</ref> A reviewer writes that the book "...is truly a classic. It presents the theory of dimension for separable metric spaces with what seems to be an impossible mixture of depth, clarity, precision, succinctness, and comprehensiveness."
Hurewicz is best remembered for three remarkable contributions to mathematics: his discovery of the [[higher homotopy groups]] in 1935-36, his discovery of the [[Homotopy long exact sequence#Long exact sequence of a fibration|long exact homotopy sequence]] for fibrations in 1941, and the [[Hurewicz theorem]] connecting homotopy and homology groups. His work led to [[homological algebra]]. It was during Hurewicz's time as Brouwer's assistant in Amsterdam that he did the work on the higher homotopy groups; "...the idea was not new, but until Hurewicz nobody had pursued it as it should have been. Investigators did not expect much new information from [[Group (mathematics)|groups]], which were obviously [[commutative]]..."
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* {{MacTutor Biography|id=Hurewicz}}
* {{MathGenealogy|id=5856}}
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* Krystyna Kuperberg (ed.): ''[http://www.ams.org/bookstore?fn=20&arg1=geotopo&ikey=CWORKS-4 Collected Works of Witold Hurewicz]'', 1995, ISBN 0-8218-0011-6
* {{DNB-Portal|11945291X}}
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{{Persondata <!-- Metadata: see [[Wikipedia:Persondata]]. -->
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