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Tietze extension theorem
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==History== [[L. E. J. Brouwer]] and [[Henri Lebesgue]] proved a special case of the theorem, when <math>X</math> is a finite-dimensional real [[vector space]]. [[Heinrich Tietze]] extended it to all [[metric space]]s, and [[Pavel Samuilovich Urysohn|Pavel Urysohn]] proved the theorem as stated here, for normal topological spaces.<ref>{{springer|title=Urysohn-Brouwer lemma|id=p/u095860}}</ref><ref>{{citation|first=Paul|last=Urysohn|author-link=Pavel Samuilovich Urysohn|journal=[[Mathematische Annalen]]|year=1925|volume=94|issue=1|pages=262–295|title=Über die Mächtigkeit der zusammenhängenden Mengen|doi=10.1007/BF01208659|hdl=10338.dmlcz/101038|hdl-access=free}}.</ref>
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