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...
-spaces and the Wallman compactification.
The disjoint arcs property for homogeneous curves
The local structure of homogeneous continua (curves) is studied. Components of open subsets of each homogeneous curve which is not a solenoid have the disjoint arcs property. If the curve is aposyndetic, then the components are nonplanar. A new characterization of solenoids is formulated: a continuum is a solenoid if and only if it is homogeneous, contains no terminal nontrivial subcontinua and small subcontinua are not ∞-ods.
The generalized Schoenflies theorem for absolute suspensions
The aim of this paper is to prove the generalized Schoenflies theorem for the class of absolute suspensions. The question whether the finite-dimensional absolute suspensions are homeomorphic to spheres remains open. Partial solution to this question was obtained in [Sz] and [Mi]. Morton Brown gave in [Br] an ingenious proof of the generalized Schoenflies theorem. Careful analysis of his proof reveals that modulo some technical adjustments a similar argument gives an analogous result for the class...
The Menger curve Characterization and extension of homeomorphisms of non-locally-separating closed subsets [Book]
The topology of the unit interval is not uniquely determined by its continuous self maps among set systems
Topological spaces with a linear basis
Topologies defined by some invariant pseudodistances
Trivial bundles and near-homeomorphisms
Unique -closure for some -groups of rational valued functions
Usually, an abelian -group, even an archimedean -group, has a relatively large infinity of distinct -closures. Here, we find a reasonably large class with unique and perfectly describable -closure, the class of archimedean -groups with weak unit which are “-convex”. ( is the group of rationals.) Any is -convex and its unique -closure is the Alexandroff algebra of functions on defined from the clopen sets; this is sometimes .
Universal meager -sets in locally compact manifolds
In each manifold modeled on a finite or infinite dimensional cube , , we construct a meager -subset which is universal meager in the sense that for each meager subset there is a homeomorphism such that . We also prove that any two universal meager -sets in are ambiently homeomorphic.
Wallman compactification and zero-dimensionality.
Zur Lage null- und eindimensionaler Punktmengen im
О продолжении отображений в сферы и о счетных разложениях тихоновских кубов
О пространствах, близких .