Mappings of terminal continua (Q1608211)

Nonseparating subcontinua have been studied by a number of authors and the term ``terminal'' has been used for a variety of nonseparating subcontinua. In their expository paper, \textit{D. E. Bennett} and \textit{J. B. Fugate} [Diss. Math. 149, 1-46 (1977; Zbl 0354.54017)] investigated these various concepts of nonseparating subcontinua. \textit{G. R. Gordh jun.} [Pac. J. Math. 47, 457-464 (1973; Zbl 0262.54032)] introduced the concept of terminal subcontinua for hereditarily unicoherent continua by defining a subcontinuum \(K\) of a hereditarily unicoherent continuum \(K\) to be terminal provided (1) \(K\) is contained in an irreducible subcontinuum of \(X\) and (2) for each subcontinuum \(I\) of \(X\) containing \(K\), there is a point \(x\in X\) such that \(I\) is irreducible about \(K\cup\{x\}\). In this paper the author applies Gordh's concept of terminal subcontinua to arbitrary continua and mapping properties of these two concepts are investigated. In particular, it is shown that invariance of terminality holds for atomic mappings. This extends the author's work [Commentat. Math. Univ. Carolin. 32, No. 2, 377-382 (1991; Zbl 0753.54017)] on some mapping properties of other nonseparating subcontinua.