Extremal continua: A class of non-separating subcontinua (Q1079840)

The notion of a terminal continuum, as defined by \textit{D. E. Bennett} and \textit{J. B. Fugate} [Diss. Math. 149 (1977; Zbl 0354.54017)] is used to introduce extremal continua, a class of non-separating subcontinua of a continuum. An extremal continuum can be characterized as a proper subcontinuum Y of a metric continuum x with the property that Y contains a point of irreducibility of each irreducible subcontinuum of X that meets Y. If Y is an extremal subcontinuum of X, then Y does not separate any subcontinuum of X containing Y; moreover, if Y is a proper subcontinuum of X and Y does not cut any subcontinuum of X containing Y, then Y is extremal in X.