On monomorphic topological functors with finite supports

  • 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
Published online: 2012-06-28

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.

How to Cite
(1)
BanakhT., MartynenkoM., ZarichnyiM. On Monomorphic Topological Functors With Finite Supports. Carpathian Math. Publ. 2012, 4 (1), 4-11.