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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.

Worked example · 12 - 30 + 20

Arithmetic · Arithmetic

Evaluate 12 - 30 + 20

12 - 30 + 20

Step by step

  1. -30 + 12 + 20 = 2

    Add: -30 + 12 + 20 = 2.

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How to: Homeomorphism and topological invariants

  1. Add: -30 + 12 + 20 = 2.

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