On monomorphic topological functors with finite supports

Array

Authors

  • T.O. Banakh Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine
  • M.V. Martynenko Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine
  • M.M. Zarichnyi Ivan Franko Lviv National University, 1 Universytetska str., 79000, Lviv, Ukraine

Keywords:

monomorphic functor, finite support, functor of finite degree

Abstract

We prove that a monomorphic functor $F:\mathbf{Comp}\to\mathbf{Comp}$ with finite supports is epimorphic, continuous, and its maximal  $\varnothing$-modification $F^\circ$ preserves intersections. This implies that a monomorphic functor $F:\mathbf{Comp}\to\mathbf{Comp}$ of finite degree $\deg F\le n$ preserves (finite-dimensional) compact ANRs if the spaces $F\varnothing$, $F^\circ\varnothing$ and $Fn$ are finite-dimensional ANRs. This improves a known result of Basmanov.

Downloads

Published

2012-06-28

How to Cite

(1)
Banakh, T.; Martynenko, M.; Zarichnyi, M. On Monomorphic Topological Functors With Finite Supports: Array. Carpathian Math. Publ. 2012, 4, 4-11.

Issue

Section

Scientific articles