ALL libraries (COBIB.SI union bibliographic/catalogue database)
13.
On universality of countable and weak products of sigma hereditarily disconnected spaces
Banakh, Taras, 1968- ; Cauty, Robert, 1946-
Suppose a metrizable separable space ▫$Y$▫ is sigma hereditarily disconnected, i.e., it is a countable union of hereditarily disconnected subspaces. We prove that the countable power ▫$X^\omega$▫ of ...any subspace ▫$X \subset Y$▫ is not universal for the class ▫${\cal A}_2$▫ of absolute ▫$G_{\delta \sigma }$▫-sets; moreover, if ▫$Y$▫ is an absolute ▫$F_{\sigma \delta }$▫-set, then ▫$X^\omega$▫ contains no closed topological copy of the Nagata space ▫${\cal N} = W(I,{\mathbbP})$▫; if ▫$Y$▫ is an absolute ▫$G_\delta$▫-set, then ▫$X^\omega$▫ contains no closed copy of the Smirnov space ▫${\sigma} = W(I,0)$▫. On the other hand, the countable power ▫$X^\omega$▫ of any absolute retract of the first Baire category contains a closed topological copy of each ▫${\sigma }$▫-compact space having a strongly countable-dimensional completion. We also prove that for a Polish space ▫$X$▫ and a subspace ▫$Y \subset X$▫ admitting an embedding intoa ▫${\sigma }$▫-compact sigma hereditarily disconnected space ▫$Z$▫ the weak product ▫$W(X,Y) = \{ (x_i) \in X^\omega :$▫ almost all ▫$x_i\in Y\} \subset X^\omega$▫ is not universal for the class ▫${\cal M}_3$▫ of absolute ▫$G_{\delta \sigma \delta }$▫-sets; moreover, if the space ▫$Z$▫ is compact then ▫$W(X,Y)$▫ is not universal for the class ▫${\cal M}_2$▫ of absolute ▫$F_{\sigma \delta}$▫-sets.
It was not necessary to add the material to the shelf.
Bibliographic material was successfully added on shelf.
Adding bibliographical material on shelf was not successful.
Material is already on the shelf.
Permalink
URL:
Impact factor
Access to the JCR database is permitted only to users from Slovenia. Your current IP address is not on the list of IP addresses with access permission, and authentication with the relevant AAI accout is required.
Year
Impact factor
Edition
Category
Classification
JCR
SNIP
JCR
SNIP
JCR
SNIP
JCR
SNIP
Select the library membership card:
DRS,
in which the journal is indexed
Database name
Field
Year
Links to authors' personal bibliographies
Links to information on researchers in the SICRIS system
Subject headings in COBISS General List of Subject Headings
Select pickup location
The material from the parent unit is free. If the material is delivered to the pickup location from another unit, the library may charge you for this service.
