DMS Continuum Theory/Set Theoretic Topology Seminar

Speaker: David Lipham

Abstract: We construct a connected space with a dispersion point which has a basis of open sets with discrete boundaries.  By a result of Tymchatyn, it embeds into a rational continuum.  A continuum is rational if it has a basis of open sets with countable boundaries.  This should answer a question of Grispolakis & Tymchatyn (c. 1975/1977). The example generates an indecomposable connected set which also embeds into a rational continuum.  On the other hand, we prove that no indecomposable semicontinuum can be embedded into a rational continuum.”