Glasnik Matematicki, Vol. 36, No.2 (2001), 223-232.

LOCAL CONNECTEDNESS AND UNICOHERENCE AT SUBCONTINUA

Deborah Oliveros and Isabel Puga

Instituto de Matematicas, UNAM, Circuito exterior C.U. Mexico D.F. 04510, Mexico
e-mail: deborah@math.ucalgary.ca

Departamento de Matematicas, Faculdad de Ciencias, UNAM, Circuito exterior C.U. Mexico D.F. 04510, Mexico
e-mail: ipe@hp.fciencias.unam.mx


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.

1991 Mathematics Subject Classification.   54F20, 54F55.

Key words and phrases.   Unicoherence, unicoherence at subcontinua, strangled, cyclic element, local connectedness, semilocal connectedness.


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