Analysis on Metric Space Q

Details Analysis on Metric Space Q Analysis on Metric Space Q

2006-07-21

arxiv.org/abs/math/0607560v2

Mathematics

General Topology

24 pages

Scientific paper

In this paper, we show that the metric space Q is a positively-curved space (PC-space) in the sense of Alexandrov. We also discuss some issues like metric tangent cone and exponential map of Q. Then we give a stratification of this metric space according to the signature of points in Q. Some properties of this stratification are shown. The second part of this paper is devoted to some basic analysis on the space Q, like the tensor sum and L-p space, which can be of independent interest. In the end, we give another definition of derivative for multiple-valued functions, which is equivalent to the one used by Almgren. An interesting theorem about regular selection of multiple-valued functions which preserves the differentiability concludes this paper.

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