#### 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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