拓扑空间上的Lipschitz函数
Lipschitz functions on topometric spaces
摘要：
我们研究函数的拓扑空间都（度量）Lipschitz和（拓扑）连续，使用它们的上下文中，在经典拓扑，普通连续函数使用。我们研究的关系，这样的功能与拓扑版本的经典分离公理，即正规性和完全正则性，以及与拓扑空间的完善。我们还恢复了一个紧凑的拓扑空间$X$从连续$1$ -Lipschitz函数的$X$上的格，在类似的恢复一个紧凑的拓扑空间$X$从结构（实或复）功能$X$。
英文摘要：
We study functions on topometric spaces which are both (metrically) Lipschitz and (topologically) continuous, using them in contexts where, in classical topology, ordinary continuous functions are used. We study the relations of such functions with topometric versions of classical separation axioms, namely, normality and complete regularity, as well as with completions of topometric spaces. We also recover a compact topometric space $X$ from the lattice of continuous $1$-Lipschitz functions on $X$, in analogy with the recovery of a compact topological space $X$ from the structure of (real or complex) functions on $X$.
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