The empty set is
contractible, meaning it can be continuously deformed to a single point.
空集是可收缩的,意味着它可以连续地变形到一个点。
A solid sphere is not
contractible to a point, unlike a hollow sphere which is.
实心球不能收缩到一点,而空心球则可以。
In topology, a disk is considered
contractible because it can be shrunk to its center.
在拓扑学中,圆盘被认为是可收缩的,因为它可以收缩到它的中心点。
A
contractible space has the homotopy type of a point.
一个可收缩的空间在同伦型上等价于一个点。
The figure eight space is not
contractible; it has nontrivial fundamental group.
“8”字空间不是可收缩的;它有一个非平凡的基本群。
Contractible complexes in algebraic topology simplify many computations.
代数拓扑中的可收缩复形简化了许多计算。
A cube can be continuously deformed into a ball, showing it's also
contractible.
立方体可以连续变形为球体,表明它也是可收缩的。
The concept of contractibility helps distinguish spaces with different topological properties.
可收缩性这一概念有助于区分具有不同拓扑性质的空间。
Even a very twisted and convoluted path in space can become a point if the space is
contractible.
即使在空间中路径非常扭曲和复杂,如果该空间是可收缩的,它也可以变为一个点。
Contractibility is a key property in understanding fixed point theory in mathematics.
可收缩性是理解数学中不动点理论的关键性质。
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