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Τι (ποιος) είναι differentiable homotopy - ορισμός

WEAK DERIVATION

Weakly Differentiable; Weakly differentiable

Homotopy

CONTINUOUS DEFORMATION BETWEEN TWO CONTINUOUS MAPS

Homotopic; Homotopy equivalent; Homotopy equivalence; Homotopy invariant; Homotopy class; Null-homotopic; Homotopy type; Nullhomotopic; Homotopy invariance; Homotopy of maps; Homotopically equivalent; Homotopic maps; Homotopy of paths; Homotopical; Homotopy classes; Null-homotopy; Null homotopy; Nullhomotopic map; Null homotopic; Relative homotopy; Homotopy retract; Continuous deformation; Relative homotopy class; Homotopy-equivalent; Homotopy extension and lifting property; Isotopy (topology); Homotopies

In topology, a branch of mathematics, two continuous functions from one topological space to another are called homotopic (from "same, similar" and "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy (, ; , ) between the two functions. A notable use of homotopy is the definition of homotopy groups and cohomotopy groups, important invariants in algebraic topology.

https://en.wikipedia.org/wiki/Homotopy

Differentiable function

$The function <math>f : \R \to \R</math> with <math>f(x) = x^2\sin\left(\tfrac 1x\right)</math> for <math>x \neq 0</math> and <math>f(0) = 0</math> is differentiable. However, this function is not continuously differentiable.$

FUNCTION WHOSE DERIVATIVE EXISTS AT EACH POINT IN ITS DOMAIN

Differentiability; Differentiable; Continuously differentiable; Differentiabillity; Continuously differentiable function; Local linearity; Differentiable map; Nowhere differentiable; Continuous differentiability; Differentiability of a function; Differentiable functions; Differentiable mapping; Derivable function; Differentiable (function)

In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain.

https://en.wikipedia.org/wiki/Differentiable_function

Differential structure

MATHEMATICAL STRUCTURE

Differentiable structure

In mathematics, an n-dimensional differential structure (or differentiable structure) on a set M makes M into an n-dimensional differential manifold, which is a topological manifold with some additional structure that allows for differential calculus on the manifold. If M is already a topological manifold, it is required that the new topology be identical to the existing one.

https://en.wikipedia.org/wiki/Differential_structure

Βικιπαίδεια

Weak derivative

In mathematics, a weak derivative is a generalization of the concept of the derivative of a function (strong derivative) for functions not assumed differentiable, but only integrable, i.e., to lie in the L^p space $L^{1}([a,b])$ .

The method of integration by parts holds that for differentiable functions $u$ and $\varphi$ we have

{\begin{aligned}\int _{a}^{b}u(x)\varphi '(x)\,dx&={\Big [}u(x)\varphi (x){\Big ]}_{a}^{b}-\int _{a}^{b}u'(x)\varphi (x)\,dx.\\[6pt]\end{aligned}}

A function u' being the weak derivative of u is essentially defined by the requirement that this equation must hold for all infinitely differentiable functions φ vanishing at the boundary points ( $\varphi (a)=\varphi (b)=0$ ).

https://en.wikipedia.org/wiki/Weak derivative