Sentence examples for maps of degree from inspiring English sources

Let be the ech homology functor with compact carriers and coefficients in the field of rational numbers from the category of Hausdorff topological spaces and continuous maps to the category of graded vector spaces and linear maps of degree zero.

Let us also denote by (operatorname {Vect}_{G}) the category of graded vector spaces over the field of rational numbers (mathbb{Q}) and linear maps of degree zero between such spaces.

Let H* be the Čech homology functor with compact carriers and coefficients in the field of rational numbers ℚ from the category of Hausdorff topological spaces and continuous maps to the category of graded vector spaces and linear maps of degree zero.

Let H be the C̆ech homology functor with compact carriers and coefficients in the field of rational numbers K from the category of Hausdorff topological spaces and continuous maps to the category of graded vector spaces and linear maps of degree zero.

The map (pr_{2}: beta_{i}rightarrowmathbb{D}_{r}), (pr_{2} x,y)=y) is a covering map of degree one.

Our objective is the following: (Conditions on degrees) Let (U^_{1}) be the escaping set of a complex Hénon mapping of degree d, with d being a prime integer.

Clearly, every homogeneous map of degree p (on a generalized cone) is positively homogeneous of the same degree p. The reverse is not always true.

Step 2: f is a map of degree one since f induces an isomorphism between the last non zero homology groups of M, N respectively.

For the analogous problem on the half-plane we prove existence of a global minimizer when p is close to 2. The key ingredient of our proof is the degree reduction argument that allows us to construct a map of degree d="1 from an arbitrary map of degree d>1 without increasing the p-Ginzburg Landau energy.

Further, the mapping f is called a generalized β-γ-type contractive mapping if it is a generalized β-γ-type contractive mapping of degree k for each (kinmathbb{N}).

We notice that if a mapping (f : X to Y) is a monomial mapping of degree n, then (f(rx) = r^{n} f(x)) for all (x in X) and all rational numbers r (see [1, 2]).