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Glite Dictionary
💪 Can get smaller 🔵 Can shrink fully 🤒 Able to catch
contractible

contractible

9.9
Can shrink into a single point without cutting or breaking
  • adjective
  • /kənˈtræktəbl/
  • Specialized
translation icon : contractible
  • The mathematician explained why the space was contractible using a simple deformation.

Examples

  • A shape is contractible.

  • If a space is contractible, it has the same homotopy type as a point.

  • In algebraic topology, a sphere is not contractible but a disk is.

  • This space is contractible!

  • In topology, a space is considered contractible if it can be continuously shrunk to a single point without tearing.

  • The mathematicians proved that the shape was contractible to a point through a series of transformations.

  • To understand many concepts in topology, it helps to visualize objects that are contractible to a single point.

Surface Forms

contractible positive

Morphology

contractible = contract (opaque) = contract + ible

Although morphologically 'contract' + '-ible', the topological meaning ('reducible to a point') is a specialized technical sense not inferable by typical learners.

Etymology

Contractible comes from the Latin root contrahere, from con- 'together' and trahere 'to pull', the same idea behind contract. So in math, a space is contractible because it can be 'pulled together' to a single point, which is why the word means 'can be reduced to a point'.