Electronic Version 17 (1992), 391-393

Sergio Macías

We announce the proofs of the following theorems:

Theorem 1. Let X be a homogeneous continuum essentially embedded in \Gamma. If [( K)\tilde] is a component of [X\tilde] and if [( K)\tilde] _C is a continuum component of [X\tilde], then [( K)\tilde],[( K)\tilde] _C, \sigma([( K)\tilde]), and \sigma([( K)\tilde] _C) are homogeneous.

Theorem 2. Assume the hypothesis of Theorem 1. If X is also one-dimensional, then \sigma([( K)\tilde]) and \sigma([( K)\tilde] _C) are dense in X.

Theorem 3. There exists a homogeneous continuum X and distinct embeddings of X in \Gamma such that the components of [X\tilde] of the corresponding embeddings are nonhomeomorphic. The images of such components under the covering maps are not homeomorphic either.

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