A characterization of locally connected continua by hyperspace retractions
A characterization of locally connected continua by hyperspace retractions
Let <italic>X</italic> be a (metric) continuum. It is shown that <italic>X</italic> is locally connected if and only if there is special type of retraction from <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2 Superscript upper X"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mn>2</mml:mn> <mml:mi>X</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{2^X}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> onto <inline-formula content-type="math/mathml"> <mml:math …