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MiS Preprint
81/2011

Note on a compactness characterization via a pursuit game

Miroslav Bačák

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.

Received:
Dec 9, 2011
Published:
Dec 9, 2011
Keywords:
evasion-pursuit game, Nonpositive curvature, compactness

Related publications

inJournal
2012 Repository Open Access
Miroslav Bačák

Note on a compactness characterization via a pursuit game

In: Geometriae dedicata, 160 (2012) 1, pp. 195-197