Sul la theorie de la dimension dans les hypergroupes
Sur la caractérisation topologique des compacts à l'aide des demi-treillis des pseudométriques continues
For a Tikhonov space X we denote by Pc(X) the semilattice of all continuous pseudometrics on X. It is proved that compact Hausdorff spaces X and Y are homeomorphic if and only if there is a positive-homogeneous (or an additive) semi-lattice isomorphism T:Pc(X) → Pc(Y). A topology on Pc(X) is called admissible if it is intermediate between the compact-open and pointwise topologies on Pc(X). Another result states that Tikhonov spaces X and Y are homeomorphic if and only if there exists a positive-homogeneous...
Sur la classificaton des continus héréditairment unicohérents
Sur le nombre de côtés d'une sous-variété
Sur les rétractes absolus Pn -valués de dimension finie
We prove that a k-dimensional hereditarily indecomposable metrisable continuum is not a -valued absolute retract. We deduce from this that none of the classical characterizations of ANR (metric) extends to the class of stratifiable spaces.
Sur l’invariance de la dimension infinie forte par t-équivalence
Let X and Y be metric compacta such that there exists a continuous open surjection from onto . We prove that if there exists an integer k such that is strongly infinite-dimensional, then there exists an integer p such that is strongly infinite-dimensional.
Sur un continu acyclique qui se laisse transformer topologiquement en lui même sans points invariants