In this paper -spaces are introduced and studied. They are a common generalization of Lindelöf spaces and -spaces researched by E. Michael. A space is called an -space if, whenever is a closed cover of with compact, then or is Lindelöf. Semi-strong -spaces and strong -spaces are also defined and investigated. It is demonstrated that the three spaces are different and have interesting properties and behaviors.
Soit une application analytique propre entre des ouverts de , soit un sous-ensemble analytique de et soit . On donne des conditions pour que soit de codimension 1 dans .
We show that a natural quotient of the projective Fraïssé limit of a family that consists of finite rooted trees is the Lelek fan. Using this construction, we study properties of the Lelek fan and of its homeomorphism group. We show that the Lelek fan is projectively universal and projectively ultrahomogeneous in the class of smooth fans. We further show that the homeomorphism group of the Lelek fan is totally disconnected, generated by every neighbourhood of the identity, has a dense conjugacy...
We give an example of a uniform quotient map from R2 to R which has non-locally connected level sets.
In accordance with the Bing-Borsuk conjecture, we show that if X is an n-dimensional homogeneous metric ANR continuum and x ∈ X, then there is a local basis at x consisting of connected open sets U such that the cohomological properties of Ū and bd U are similar to the properties of the closed ball ⁿ ⊂ ℝⁿ and its boundary . We also prove that a metric ANR compactum X of dimension n is dimensionally full-valued if and only if the group Hₙ(X,X∖x;ℤ) is not trivial for some x ∈ X. This implies that...
In the first part of the paper behavior of conditions related to local connectivity at a point is discussed if the space is transformed under a mapping that is interior or open at the considered point of the domain. The second part of the paper deals with metric locally connected continua. They are characterized as continua for which the hyperspace of their nonempty closed subjects is homogeneous with respect to open mappings. A similar characterization for the hyperspace of subcontinua remains...