Relaciones entre orden, normalidad y completa regularidad.
We study some relations whose compatibility with the topology is equivalent to normality or to complete regularity.
Relative directed homotopy theory of partially ordered spaces.
Remarks on a conjecture of Hartshorne.
Remarks on characterization of dimension of separable metrizable spaces
Remarks on non-planable dendroids
Remarks on some class of continuous mappings of λ-dendroids
Remarks on the absolute suspension
Remarks on the sobriety of Scott topology and weak topology on posets
We give some necessary and sufficient conditions for the Scott topology on a complete lattice to be sober, and a sufficient condition for the weak topology on a poset to be sober. These generalize the corresponding results in [1], [2] and [4].
Remarks on topologies uniquely determined by their continuous self maps
Removing sets from connected product spaces while preserving connectedness
As per the title, the nature of sets that can be removed from a product of more than one connected, arcwise connected, or point arcwise connected spaces while preserving the appropriate kind of connectedness is studied. This can depend on the cardinality of the set being removed or sometimes just on the cardinality of what is removed from one or two factor spaces. Sometimes it can depend on topological properties of the set being removed or its trace on various factor spaces. Some of the results...
Research Article. Multiscale Analysis of 1-rectifiable Measures II: Characterizations
A measure is 1-rectifiable if there is a countable union of finite length curves whose complement has zero measure. We characterize 1-rectifiable Radon measures μ in n-dimensional Euclidean space for all n ≥ 2 in terms of positivity of the lower density and finiteness of a geometric square function, which loosely speaking, records in an L2 gauge the extent to which μ admits approximate tangent lines, or has rapidly growing density ratios, along its support. In contrast with the classical theorems...
Residuality of the set of embeddings into Nagata's n-dimensional universal spaces
Resolving a question of Arkhangel'skiĭ's
We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.
Retracting fans onto finite fans
Retral spaces and continua with the fixed point property
We show that every retral continuum with the fixed point property is locally connected. It follows that an indecomposable continuum with the fixed point property is not a retract of a topological group.
Rigid extensions of -groups of continuous functions
Let , and denote the -groups of integer-valued, rational-valued and real-valued continuous functions on a topological space , respectively. Characterizations are given for the extensions to be rigid, major, and dense.
Rozklad elementární křivky na Jordanovy křivky
Sätze aus der Functionentheorie
Selection theorems for partitions of Polish spaces
Selections and approaching points in products
The present paper aims to furnish simple proofs of some recent results about selections on product spaces obtained by García-Ferreira, Miyazaki and Nogura. The topic is discussed in the framework of a result of Katětov about complete normality of products. Also, some applications for products with a countably compact factor are demonstrated as well.