Sentence examples for continuous map between from inspiring English sources

Assume that (f : M rightarrow N) is a continuous map between two compact Kähler manifolds and that the curvature tensor of N is strongly negative.

Let be a continuous map between Hausdorff, normal, connected, locally path connected, and semilocally simply connected spaces, and let be a given base point.

Moreover, this correspondence is functorial: any Boolean homomorphism is sent to a continuous map of topological spaces, and, conversely, any continuous map between the spaces is sent to a Boolean homomorphism.

Lemma 2.4 Let F : X → Y be a continuous map between metric spaces and let { γ n } be a sequence of continuous functions from a compact interval [ a, b ] (or, more generally, from a compact space) into X.

Let us also recall that a continuous map between topological spaces is called locally compact if each point in its domain has a neighborhood whose image is contained in a compact set.

end{aligned}Note that T maps every level set (E^*cap {x_n=t}) into the level set (Bcap {x_n=tau (t)}), and it is a one-to-one continuous map between the open sets (E^*) and B. Moreover for all (0

Hence there was a category consisting of all groups and all maps between them that preserve multiplication, and there was another category of all topological spaces and all continuous maps between them.

Let f, g : M1 → M2 be continuous maps between closed oriented manifolds M1, M2 of equal dimension.

We prove practical formulas for the Reidemeister coincidence number, the Lefschetz coincidence number and the Nielsen coincidence number of continuous maps between oriented infra-nilmanifolds of equal dimension.

The following theorem gives a formula for the Lefschetz coincidence number of a pair of continuous maps between nilmanifolds of equal dimension.

In this paper, we give a homotopy classification of continuous maps between two simply connected four manifolds M,N and design an algorithm and program to give explicit computations.