diffeology

diffeology

English

Noun

diffeology (plural diffeologies)

1. (differential geometry) The set of smooth parametrizations of a given set ${\\displaystyle X}$; the set of smooth maps ${\\displaystyle S\\rightarrow X}$, where ${\\displaystyle S}$ is any open set ${\\displaystyle \\subseteq \\mathbb {R} ^{n}}$; the theory of such constructs.
   • 2007, Jan Kubarski, Geometry and Topology of Manifolds: The Mathematical Legacy of Charles Ehresmann; on the Occasion of the Hundredth Anniversary of His Birthday, page 358,

     In this case, ${\\displaystyle A}$ and ${\\displaystyle f(A)}$ are both D-open and ${\\displaystyle f:A\\rightarrow f(A)}$ is a diffeomorphism where ${\\displaystyle A}$ and ${\\displaystyle f(A)}$ are equipped with their subset diffeology.

   • 2010, Patrick Iglesias-Zemmour, The Moment Maps in Diffeology, American Mathematical Society, page 32,

     And, for ${\\displaystyle {\\mathcal {G}}^{*}/\\Gamma }$ and ${\\displaystyle {\\mathcal {G}}'^{*}/\\Gamma '}$ equipped with the quotient diffeologies, ${\\displaystyle h_{\\Gamma }^{*}}$ is naturally smooth.

Usage notes

• The dimensional qualifier n is not required to be the same for all members of the diffeology.
• A member of a diffeology may be called a plot.
• A set together with a diffeology is called a diffeological space.

Derived terms

• quotient diffeology

Related terms

• diffeological

See also

• diffeological space

Further reading

• diffeology on Wikipedia.Wikipedia