Abstract

MACIAS, SERGIO. On Type θ and θ_n continua. Integración - UIS [online]. 2015, vol.33, n.1, pp.27-39. ISSN 0120-419X.

In 1974 Professor R. W. FitzGerald defined type θ and θ_n continua. (A continuum X is of type θ (type θ_n, for some positive integer n) if for each subcontinuum K of X, we have that X \ K has only a finite number of components (X \ K has at most n components).) Professors E. E. Grace and E. J. Vought continued the study of these clases of continua, when such continua admit an upper semicontinuous monotone decomposition whose quotient space is a graph. The purpose of this work is to present some of the properties of type θ and θ_n continua, mainly when the decomposition is continuous [14]

Keywords : Continuous decomposition; continuously irreducible continuum; hyperspace; idempotency; Jones' set function T; irreducible continuum; symmetric products; type θ continuum; type θ_n continuum; type A′ θ-continuum; weakly irreducible continuum; Z-set.

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