arXiv subjects

V. Gutev

Publications and source records attributed to V. Gutev.

2 recordsLinked to original sources

arXiv2010

Sections, Selections and Prohorov's Theorem

The famous Prohorov theorem for Radon probability measures is generalized in terms of usco mappings. In the case of completely metrizable spaces this is achieved by applying a classical Michael result on the existence of usco selections for l.s.c. mappings. A similar approach works when sieve-complete spaces are considered.

math.GN↗

arXiv2001

Dense families of selections and finite-dimensional spaces

A characterization of $n$-dimensional spaces via continuous selections avoiding $Z_n$-sets is given, and a selection theorem for strongly countable-dimensional spaces is established. We apply these results to prove a generalized Ostrand's theorem and to obtain a new alternative proof of the Hurewicz formula.

math.GN↗