maths.free › Topology › Homeomorphism and topological invariants
Homeomorphism and topological invariants
When two spaces are "the same", and what numbers survive stretching.
A homeomorphism is a continuous bijection with continuous inverse. Invariants (number of components, Euler characteristic V − E + F, number of holes) are the same for homeomorphic spaces, so differing invariants prove two spaces differ. Picture it: the sphere (χ = 2) against the torus (χ = 0). Think it: algebraic topology is the systematic manufacture of such invariants.
工作范例 · 12 - 30 + 20
一步
- -30 + 12 + 20 = 2
Add: -30 + 12 + 20 = 2.
发送答案
现在轮到你 选择问题, 输入或绘制您自己的 。 每一步, 图片, 答案隐藏到您询问 。
此处所用符号
输入完整定义、图片和其中每个字母的含义的符号。
如何: Homeomorphism and topological invariants
- Add: -30 + 12 + 20 = 2.
人们对人们提出的问题
Why "a doughnut is a coffee cup"?
Each can be deformed into the other without cutting or gluing: one hole each. Topology studies exactly the properties such deformations preserve.
What is compactness for?
It is the property that makes "every sequence has a convergent subsequence" and "continuous functions attain their maximum" true. On the real line it means closed and bounded.