On gate continua and their applications to study absolute retracts
by
Janusz J. Charatonik
University of Wroclaw, Wroclaw, Poland and UNAM, Mexico, Mexico

For a given class K of continua a subcontinuum K of a continuum X is called a gate continuum in X for K provided that there exists a continuum Y in K such that X \cup Y in K, Y \X =/= \emptyset, and X \cap Y in K. The concept extends the one on an end point introduced by Bing for arc-like continua. Gate continua in members of the following classes K are characterized: (hereditarily decomposable) arc-like, hereditarily irreducible, atriodic, and containing no n-od. The characterizations are used to construct absolute terminal continua for K, i.e., continua X in K that are terminal in Y in K whenever X subset Y. Applications to study some properties of absolute retracts in K are given.

All the results are obtained jointly by W. J. Charatonik, J. R. Prajs and the author. The detailed proofs will appear in Houston J. Math.

Date received: February 5, 2001