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diffeomorphism
difeomorfismo

this is true in particular when ϕ is a diffeomorphism.
this is true in particular when "φ" is a diffeomorphism.

this is an example of a homeomorphism that is not a diffeomorphism.
this is an example of a homeomorphism that is not a diffeomorphism.

every diffeomorphism is a homeomorphism, but not every homeomorphism is a diffeomorphism.
thus every diffeomorphism is a homeomorphism, but the converse is false: not every homeomorphism is a diffeomorphism.

; sixth remarka differentiable bijection is "not" necessarily a diffeomorphism.
a differentiable bijection is "not" necessarily a diffeomorphism, e.g.

===connectedness===for manifolds, the diffeomorphism group is usually not connected.
===connectedness===for manifolds the diffeomorphism group is usually not connected.

also, the differential of a local diffeomorphism is a linear isomorphism of tangent spaces.
asimismo, la aplicación diferencial de un difeomorfismo local es un isomorfismo lineal de espacios vectoriales tangentes.

more generally, the diffeomorphism group acts transitively on the configuration space "ckm".
more generally, the diffeomorphism group acts transitively on the configuration space "ckm".

* for a finite set of points, the diffeomorphism group is simply the symmetric group.
* for a finite set of points, the diffeomorphism group is simply the symmetric group.

moreover, the transition maps from one chart of this atlas to another are smooth, making the diffeomorphism group into a banach manifold.
moreover, the transition maps from one chart of this atlas to another are smooth, making the diffeomorphism group into a banach manifold.

moreover, the diffeomorphism group of the circle has the homotopy-type of the orthogonal group o(2).
moreover, the diffeomorphism group of the circle has the homotopy-type of the orthogonal group o(2).

===homotopy types===* the diffeomorphism group of s2 has the homotopy-type of the subgroup o(3).
===homotopy types===* the diffeomorphism group of s2 has the homotopy-type of the subgroup o(3).

===transitivity===for a connected manifold "m", the diffeomorphism group acts transitively on "m".
===transitivity===for a connected manifold "m" the diffeomorphism group acts transitively on "m".

* the diffeomorphism group of euclidean space r"n" consists of two components, consisting of the orientation preserving and orientation reversing diffeomorphisms.
* the diffeomorphism group of euclidean space r"n" consists of two components, consisting of the orientation preserving and orientation reversing diffeomorphisms.

* the homotopy-type of diffeomorphism groups of "n"-manifolds for "n" > 3 are poorly undersood.
* the homotopy-type of diffeomorphism groups of "n"-manifolds for "n" > 3 are poorly undersood.

"f" : "m" → "n" is called a diffeomorphism if, in coordinate charts, it satisfies the definition above.
now, "f" : "m" → "n" is called a diffeomorphism if in coordinates charts it satisfies the definition above.