Proximinality in geodesic spaces
Proximinality in geodesic spaces
Let <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math> be a complete CAT<mml:math id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> space with the geodesic extension property and Alexandrov curvature bounded below. It is shown that if <mml:math id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>C</mml:mi></mml:math> is a closed subset of <mml:math id="E4" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:math> then the set of points of <mml:math id="E5" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>X</mml:mi></mml:math> which have a unique …