Original scientific paper

Local connctedness and unicoherence at subcontinua

Deborah Oliveros
Isabel Puga

Abstract

Let X be a continuum and Y a subcontinuum of X. The purpose of this paper is to investigate the relation between the conditions "X is unicoherent at Y" and "Y is unicoherent". We say that X is strangled by Y if the closure of each component of X \ Y intersects Y in one single point. We prove: If X is strangled by Y and Y is unicoherent then X is unicoherent at Y. We also prove the converse for a locally connected (not necessarily metric) continuum X.

Keywords

Unicoherence; unicoherence at subcontinua; strangled; cyclic element; local connectedness; semilocal connectedness

Hrčak ID:

4835

URI

https://hrcak.srce.hr/4835

Publication date:

1.12.2001.

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