Sobrification of partially ordered sets.
Some Baire category type theorems for
Some order theoretic characterizations of the 3-cell
Spaces of continuous functions, box products and almost--resolvable spaces
A dense-in-itself space is called -discrete if the space of real continuous functions on with its box topology, , is a discrete space. A space is called almost--resolvable provided that is the union of a countable increasing family of subsets each of them with an empty interior. We analyze these classes of spaces by determining their relations with -resolvable and almost resolvable spaces. We prove that every almost--resolvable space is -discrete, and that these classes coincide in...
Strongly paracompact metrizable spaces
Strongly paracompact metrizable spaces are characterized in terms of special S-maps onto metrizable non-Archimedean spaces. A similar characterization of strongly metrizable spaces is obtained as well. The approach is based on a sieve-construction of "metric"-continuous pseudo-sections of lower semicontinuous mappings.
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...