自相似性的一般理论
A general theory of self-similarity
摘要：
一个鲜为人知的和非常经济的实区间[0，1]的特征，主要是由于弗洛伊德，指出区间同胚的两个副本本身粘在一起，并在精确的意义上，是普遍的。其他熟悉的空间也有类似的泛性质;例如，拓扑单形Delta^n可以定义为允许重心重分的空间的普适族。我们开发了一个一般的理论，这样的普遍特征。这也可以看作是联立线性方程理论的一种分类。我们研究方程组，其中变量代表空间，每个空间都等同于其他空间的粘合。人们寻求满足方程的泛空间族。我们回答了所有的基本问题，这样的系统，给出了一个明确的条件相当于存在一个普遍的解决方案，并明确建设时，它确实存在。
英文摘要：
A little-known and highly economical characterization of the real interval [0, 1], essentially due to Freyd, states that the interval is homeomorphic to two copies of itself glued end to end, and, in a precise sense, is universal as such. Other familiar spaces have similar universal properties; for example, the topological simplices Delta^n may be defined as the universal family of spaces admitting barycentric subdivision. We develop a general theory of such universal characterizations. This can also be regarded as a categorification of the theory of simultaneous linear equations. We study systems of equations in which the variables represent spaces and each space is equated to a gluing-together of the others. One seeks the universal family of spaces satisfying the equations. We answer all the basic questions about such systems, giving an explicit condition equivalent to the existence of a universal solution, and an explicit construction of it whenever it does exist.
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