Urysohn空间与Gurarij空间上的泛与齐次结构
一般拓扑
2018-02-09 v3 泛函分析
逻辑
摘要
利用Fraïssé理论方法，我们通过泛与齐次闭关系、收缩、Urysohn空间自身与某个固定紧度量空间的乘积的闭子集、到固定Polish度量空间的L-Lipschitz映射，丰富了Urysohn泛空间。后者提升为Urysohn空间Lipschitz自由空间上的范数为L的泛线性算子。此外，我们通过泛与齐次闭子空间和到1-补子空间的范数一投影丰富了Gurarij空间。我们通过经典的Fraïssé理论方法构造了Gurarij空间。
引用
@article{arxiv.1503.05204,
title = {Universal and homogeneous structures on the Urysohn and Gurarij spaces},
author = {Michal Doucha},
journal= {arXiv preprint arXiv:1503.05204},
year = {2018}
}
备注
This paper contains new proofs and extends the results of the earlier draft arXiv:1305.0501. In the version 2, some arguments were improved. The third version contains updated information about the author's grant