For a separable metric space X, we consider possibilities for the sequence S{X) = {dn : n G N} where dn = dim Xn. In Section 1, a general method for producing examples is given which can be used to realize many of the possible sequences. For example, there is Xn such that S{Xn) = {n, n + 1, n + 2,...}, Ynt for n > 1, such that i>(Yn) -{n,n+l,n + 2,n + 2,n + 2,...}, and Z such that S(Z) = {4,4,6,6,7,8,9,...}.In Section 2, a subset X of R2 is shown to exist which satisfies 1 = dim X - dim A and dimX3 =2.
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机译：对于可分离的度量空间X，我们考虑序列S {X）= {dn：n G N}的可能性，其中dn = dim Xn。在第1节中，给出了产生示例的通用方法，该方法可用于实现许多可能的序列。例如，存在Xn使得S {Xn）= {n，n + 1，n + 2，...}，Ynt的n> 1，使得i>（Yn）-{n，n + 1， n + 2，n + 2，n + 2，...}和Z使得S（Z）= {4,4,6,6,7,8,9，...}。在第2节中R2的子集X显示满足1 = dim X-dim A和dimX3 = 2。
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