论文标题
部分可观测时空混沌系统的无模型预测
Universal finite functorial semi-norms
论文作者
论文摘要
关于单数同源性的函数半符号衡量同源类别的“大小”。几何有意义的例子是$ \ ell^1 $ -semi-norm。但是，$ \ ell^1 $ -semi-norm并不是普遍的，因为它不会在尽可能少的类中消失。我们表明，在单数同源性上确实存在通用有限函数半按在拓扑空间的类别上，这与有限的CW-复合物相当。我们的论点还适用于功能性半norms的更一般的设置。
Functorial semi-norms on singular homology measure the "size" of homology classes. A geometrically meaningful example is the $\ell^1$-semi-norm. However, the $\ell^1$-semi-norm is not universal in the sense that it does not vanish on as few classes as possible. We show that universal finite functorial semi-norms do exist on singular homology on the category of topological spaces that are homotopy equivalent to finite CW-complexes. Our arguments also apply to more general settings of functorial semi-norms.
