The article is devoted to a generalization of Clifford and Grassmann algebras for the case of vector spaces over the field of complex numbers. The geometric interpretation of such generalizations are presented. Multieuclidean geometry is considered as well as the importance of it in physics.

It is shown that the hyperspace of a connected CW-complex is an absolute retract for stratifiable spaces, where the hyperspace is the space of non-empty compact (connected) sets with the Vietoris topology.

By Fin(X) (resp. $Fi{n}^k\left(X\right)$), we denote the hyperspace of all non-empty finite subsets of X (resp. consisting of at most k points) with the Vietoris topology. Let ℓ₂(τ) be the Hilbert space with weight τ and $\ell {₂}^f\left(\tau \right)$ the linear span of the canonical orthonormal basis of ℓ₂(τ). It is shown that if $E=\ell {₂}^f\left(\tau \right)$ or E is an absorbing set in ℓ₂(τ) for one of the absolute Borel classes ${}_{\alpha }\left(\tau \right)$ and ${}_{\alpha }\left(\tau \right)$ of weight ≤ τ (α > 0) then Fin(E) and each $Fi{n}^k\left(E\right)$ are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X) is homeomorphic...

If X is a space then L(X) denotes the subspace of C(X) consisting of all Peano (sub)continua. We prove that for n ≥ 3 the space $L\left({ℝ}^n\right)$ is homeomorphic to $B^{\infty }$, where B denotes the pseudo-boundary of the Hilbert cube Q.

In this paper we study the hypersurfaces $M^n$ given as connected compact regular fibers of a differentiable map $f:{ℝ}^{n+1}\to ℝ$, in the cases in which $f$ has finitely many nondegenerate critical points in the unbounded component of ${ℝ}^{n+1}-M^n$.

Soit $\omega$ un germe en $0\in {\mathbf{C}}^n$ de 1-forme différentielle holomorphe, satisfaisant la condition d’intégrabilité $\omega \wedge d\omega =0$ et non dicritique, i.e. sur toute surface $Z$ non intégrale de $\omega$, on ne peut tracer, au voisinage de 0, qu’un nombre fini de germes de courbes analytiques $({\Gamma }_i,P_i)$, intégrales de $\omega$, avec $P_i\in Z\cap Sing\omega$. Alors $\omega$ possède un germe d’hypersurface analytique intégrale.