Inserting measurable functions precisely
Javier Gutiérrez García; Tomasz Kubiak
Czechoslovak Mathematical Journal (2014)
- Volume: 64, Issue: 3, page 743-749
- ISSN: 0011-4642
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topGutiérrez García, Javier, and Kubiak, Tomasz. "Inserting measurable functions precisely." Czechoslovak Mathematical Journal 64.3 (2014): 743-749. <http://eudml.org/doc/262160>.
@article{GutiérrezGarcía2014,
abstract = {A family of subsets of a set is called a $\sigma $-topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A $\sigma $-topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect $\sigma $-topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a $\sigma $-topological version of Katětov-Tong insertion theorem yields a Michael insertion theorem for normal and perfect $\sigma $-topological spaces.},
author = {Gutiérrez García, Javier, Kubiak, Tomasz},
journal = {Czechoslovak Mathematical Journal},
keywords = {insertion; $\sigma $-topology; $\sigma $-ring; perfectness; normality; upper measurable function; lower measurable function; measurable function; insertion; $\sigma $-topology; -ring; perfectness; normality; upper measurable function; lower measurable function; measurable function},
language = {eng},
number = {3},
pages = {743-749},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Inserting measurable functions precisely},
url = {http://eudml.org/doc/262160},
volume = {64},
year = {2014},
}
TY - JOUR
AU - Gutiérrez García, Javier
AU - Kubiak, Tomasz
TI - Inserting measurable functions precisely
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 3
SP - 743
EP - 749
AB - A family of subsets of a set is called a $\sigma $-topology if it is closed under arbitrary countable unions and arbitrary finite intersections. A $\sigma $-topology is perfect if any its member (open set) is a countable union of complements of open sets. In this paper perfect $\sigma $-topologies are characterized in terms of inserting lower and upper measurable functions. This improves upon and extends a similar result concerning perfect topologies. Combining this characterization with a $\sigma $-topological version of Katětov-Tong insertion theorem yields a Michael insertion theorem for normal and perfect $\sigma $-topological spaces.
LA - eng
KW - insertion; $\sigma $-topology; $\sigma $-ring; perfectness; normality; upper measurable function; lower measurable function; measurable function; insertion; $\sigma $-topology; -ring; perfectness; normality; upper measurable function; lower measurable function; measurable function
UR - http://eudml.org/doc/262160
ER -
References
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