

Preprint 81/2011
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.