A stable converse to the Vietoris-Smale theorem with applications to shape theory
A stable converse to the Vietoris-Smale theorem with applications to shape theory
Our main result says that if <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f colon upper X right-arrow upper Y"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo>:</mml:mo> <mml:mspace width="thinmathspace" /> <mml:mi>X</mml:mi> <mml:mspace width="thinmathspace" /> <mml:mo stretchy="false">→<!-- → --></mml:mo> <mml:mspace width="thinmathspace" /> <mml:mi>Y</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">f:\,X\, \to \,Y</mml:annotation> </mml:semantics> </mml:math> </inline-formula> is a map between finite polyhedra …