Resumen de Separation and connectedness in spectral compactifications

Ralph Kopperman, Richard G. Wilson

• We continue the study of the relationship between properties of an inverse spectrum and those of the inverse limit and selected subspaces of its minimal points. It is shown that limits of inverse spectra of joincompact spaces with pairwise continuous bonding maps are connected if and only if the spaces are connected. Since finite T1-spaces are discrete, there are not enough finite spaces with higher separation properties to obtain the infinite spaces with these properties as limits of inverse systems of such finite spaces.

  We show that many higher separation properties of the space of minimal points of the inverse limit result from conditions imposed on the bonding maps. This relationship is studied for the separation properties T1, regularity, complete regularity, normality and hereditary normality.