ov 2 00 2 Happy Fractals Stephen Semmes
نویسنده
چکیده
Sometimes there might be another metric space (N, ρ(u, v)) in play, and we may introduce a subscript as in BN(w, s) to indicate in which metric space the ball is defined. Let us say that a metric space (M, d(x, y)) is a happy fractal if the following three conditions are satisfied. First, M is complete as a metric space. Second, there is a constant C1 > 0 so that for each pair of points x, y in M there is a path in M connecting x to y with length at most C1 d(x, y). Third, M satisfies the doubling property that there is a constant C2 so that any ball B in M can be covered by a family of balls with half the radius of B and at most C2 elements. One might prefer the name happy metric space, since the metric space need not be fractal, as in the case of ordinary Euclidean spaces. There are
منابع مشابه
N ov 2 00 2 Happy Fractals
Sometimes there might be another metric space (N, ρ(u, v)) in play, and we may introduce a subscript as in BN(w, s) to indicate in which metric space the ball is defined. Let us say that a metric space (M, d(x, y)) is a happy fractal if the following three conditions are satisfied. First, M is complete as a metric space. Second, there is a constant C1 > 0 so that for each pair of points x, y in...
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