Note on a compactness characterization via a pursuit game

Miroslav Bačák

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Submission date: 09. Dec. 2011
Pages: 5
published in: Geometriae dedicata, 160 (2012) 1, p. 195-197 
DOI number (of the published article): 10.1007/s10711-011-9676-y
Bibtex
Keywords and phrases: evasion-pursuit game, Nonpositive curvature, compactness
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Abstract:
In [Alexander, Bishop, Ghrist: Total curvature and simple pursuit on domains of curvature bounded above. Geom. Dedicata, 2010], the authors study a pursuit-evasion game in CAT(0) spaces and arrive at the following topological characterization of the underlying CAT(0) space: the space is compact if and only if the pursuer always wins. In the present note, we, however, give an example of an unbounded CAT(0) space where the pursuer always wins, and hence strongly disprove the above statement on compactness.