| 词汇 | quasi-isometry |
| 释义 | BETA Examples of quasi-isometryquasi-isometry isn’t in the Cambridge Dictionary yet. You can help! Since any quasi-isometry between negatively curved simply connected manifolds induces a quasiconformal map of the boundaries, we have the following. Indeed, the above statement is equivalent to subgraph closure together with quasi-isometry invariance. From this, we may conclude easily that diabolicity is quasi-isometry invariant among uniformly locally finite graphs. We illustrate the consequence of quasi-isometry by the following theorems. Such a map 2 does not need to be either one-to-one or onto; however, it must be a quasi-isometry. Note that a quasi-isometry is not assumed to be continuous, for example any map between compact metric spaces is a quasiisometry. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. In advanced mathematics, quasi-isometry can be used as a criterion to state that two shapes are approximately the same. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Note that a quasi-isometry is not required to be continuous. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Formally, this means classifying finitely generated groups with their word metric up to quasi-isometry. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. Any property of metric spaces that only depends on a space's quasi-isometry class immediately yields another invariant of groups, opening the field of group theory to geometric methods. From Wikipedia This example is from Wikipedia and may be reused under a CC BY-SA license. |
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