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Invariance of domain
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==References== * {{cite book|mr=1224675|last=Bredon|first= Glen E. |title=Topology and geometry|series=Graduate Texts in Mathematics|volume= 139|publisher= [[Springer-Verlag]]|year= 1993|isbn=0-387-97926-3}} * {{cite journal|mr=4101407|last=Cao Labora|first = Daniel | title= When is a continuous bijection a homeomorphism? |journal = [[Amer. Math. Monthly]]|volume= 127 |year=2020|issue= 6|pages= 547–553| doi=10.1080/00029890.2020.1738826|s2cid=221066737 }} * {{cite journal|mr=0013313|last= Cartan |first = Henri| title=Méthodes modernes en topologie algébrique| lang=fr| journal = [[Comment. Math. Helv.]]|volume= 18 |year=1945|pages = 1–15|doi= 10.1007/BF02568096 |s2cid= 124671921 |url=https://link.springer.com/article/10.1007%2FBF02568096|url-access= subscription}} * {{cite book|mr=3887626 | last=Deo |first= Satya | title = Algebraic topology: A primer|edition= Second |series = Texts and Readings in Mathematics| volume= 27| publisher =Hindustan Book Agency| location= New Delhi | year = 2018 | isbn = 978-93-86279-67-5}} * {{cite book|mr=0658305|last=Dieudonné|first= Jean|title=Éléments d'analyse|volume= IX|series=Cahiers Scientifiques |publisher=Gauthier-Villars|location=Paris|year=1982|isbn= 2-04-011499-8|lang=fr|chapter=8. Les théorèmes de Brouwer|pages=44–47}} * {{cite book |first=Morris W. |last=Hirsch | author-link=Morris Hirsch| title=Differential Topology |location=New York |publisher=Springer |year=1988 |isbn=978-0-387-90148-0 }} (see p. 72–73 for Hirsch's proof utilizing non-existence of a differentiable retraction) * {{cite book|mr=0115161|last1=Hilton|first1= Peter J.|last2= Wylie|first2= Shaun|title=Homology theory: An introduction to algebraic topology|publisher=[[Cambridge University Press]]|location= New York |year=1960|isbn=0521094224}} * {{cite book|mr=0006493|last1=Hurewicz|first1= Witold|last2= Wallman|first2= Henry|title=Dimension Theory|series=Princeton Mathematical Series|volume= 4|publisher=[[Princeton University Press]]| year=1941|url=https://archive.org/details/in.ernet.dli.2015.84609/}} * {{cite journal|last=Kulpa|first=Władysław|title=Poincaré and domain invariance theorem|journal=Acta Univ. Carolin. Math. Phys.| volume=39|issue=1|year=1998|pages=129–136 |url=http://dml.cz/bitstream/handle/10338.dmlcz/702050/ActaCarolinae_039-1998-1_10.pdf|mr=1696596}} * {{cite book|mr=1454127 |last1=Madsen|first1= Ib |last2= Tornehave|first2= Jørgen |title=From calculus to cohomology: de Rham cohomology and characteristic classes|publisher= [[Cambridge University Press]]|year= 1997|isbn= 0-521-58059-5}} * {{cite book|mr=0198479 | last =Munkres| first = James R.|title=Elementary differential topology|series=Annals of Mathematics Studies|volume= 54 |publisher = [[Princeton University Press]]| year= 1966|edition=Revised}} * {{cite book|last=Spanier|first= Edwin H.|title=Algebraic topology|publisher= McGraw-Hill |location= New York-Toronto-London|year= 1966}} * {{cite web|url=http://terrytao.wordpress.com/2011/06/13/brouwers-fixed-point-and-invariance-of-domain-theorems-and-hilberts-fifth-problem/|title=Brouwer's fixed point and invariance of domain theorems, and Hilbert's fifth problem|first=Terence|last=Tao|author-link=Terence Tao|work=terrytao.wordpress.com|year=2011|access-date=2 February 2022}}
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