Insertion of Continuous SetValued Mappings
Abstract
An interesting insertion result about the existence of "intermediate" setvalued mappings between pairs of given setvalued mappings was obtained by Nepomnyashchii. His construction was for a paracompact domain, and he remarked that his result is similar to Dowker's insertion theorem and may represent a generalisation of this theorem. In the present paper, we characterise the $\tau$paracompact normal spaces by this insertion property and in the special case of $\tau=\omega$, i.e. for countably paracompact normal spaces, we show that it is indeed equivalent to Dowker's insertion theorem. Moreover, we obtain a similar result for $\tau$collectionwise normal spaces and show that for normal spaces, i.e. for $\omega$collectionwise normal spaces, our result is equivalent to the KatětovTong insertion theorem. Several related results are obtained as well.
 Publication:

arXiv eprints
 Pub Date:
 September 2021
 arXiv:
 arXiv:2109.12677
 Bibcode:
 2021arXiv210912677G
 Keywords:

 Mathematics  General Topology;
 54B20;
 54C30;
 54C60;
 54C65;
 54D05;
 54D15