The local structure of length spaces with curvature bounded above (Q1298009)

The author shows that different notions of dimension coincide in the case of length spaces with curvature bounded above (in the sense of Alexandrov). As one application of his methods and results, he obtains an elementary proof of a well known result by \textit{M. T. Anderson} and \textit{V. Schröder} [Invent. Math. 85, 303-315 (1986; Zbl 0615.53030)], namely that the maximal dimension of a flat in a compact space of nonpositive curvature and finite dimension is a quasi-isometry invariant. In a final chapter, the author discusses the related class of locally convex spaces.