论文标题
Brouwer固定点定理为律师
Brouwer fixed point theorem as a corollary of Lawvere
论文作者
论文摘要
研究了Brouwer固定点定理在什么意义上被视为律师定理的推论。 A suitable generalisation of the Lawvere fixed point theorem is found and a means is identified by which the Brouwer fixed point theorem can be shown to be a corollary, once an appropriate continuous surjective mapping $A' \rightarrow X^{A''}$ has been constructed for each space $X$ in a certain class of "nice" spaces for each one of which the exponential topology on $X^{A''}$ exists,在这里，$ a'$和$ a''$具有相同的载体套件，$ a'$的拓扑比$ a'$更细。结果表明，有一种自然的方式试图推导布鲁威尔作为劳维尔的推论，这是不可能的，那是没有空间$ a $ a $ a $ [0,1]^{a} $上的指数式拓扑，并且存在连续的表达$ a \ rightarrow $ a \ rightarrow [0,1]^a} a} $。然后，我们研究了从广泛的模型理论的角度出现的类似于第一个结果中描述的现象的范围，从而将问题的原始动机作为AI系统的决策理论中的原始动机的应用，这是机器智能研究所建议的问题。
It is investigated in what sense the Brouwer fixed point theorem may be viewed as a corollary of the Lawvere fixed point theorem. A suitable generalisation of the Lawvere fixed point theorem is found and a means is identified by which the Brouwer fixed point theorem can be shown to be a corollary, once an appropriate continuous surjective mapping $A' \rightarrow X^{A''}$ has been constructed for each space $X$ in a certain class of "nice" spaces for each one of which the exponential topology on $X^{A''}$ exists, and here $A'$ and $A''$ have the same carrier set and the topology on $A'$ is finer than on $A''$. It is shown that there is a certain natural way of attempting to derive Brouwer as a corollary of Lawvere which is not possible, that is there is no space $A$ for which the exponential topology on $[0,1]^{A}$ exists and there is a continuous surjection $A \rightarrow [0,1]^{A}$. We then examine the range of contexts in which phenomena like those described in the first result occur, from a broadly model-theoretic perspective, with a view towards applications for the original motivation for the problem as a problem in decision theory for AI systems, suggested by the Machine Intelligence Research Institute.
