Partial confluence of maps onto graphs and inverse limits of single graphs
Partitions of compact Hausdorff spaces
Under the assumption that the real line cannot be covered by -many nowhere dense sets, it is shown that (a) no Čech-complete space can be partitioned into -many closed nowhere dense sets; (b) no Hausdorff continuum can be partitioned into -many closed sets; and (c) no compact Hausdorff space can be partitioned into -many closed -sets.
Peano compactifications and property S metric spaces.
Period structure for pointwise periodic isometries of continua
Periodic homeomorphisms of chainable continua
Periodic homeomorphisms on T-like continua
Plane indecomposable continua no composant of which is accessible at more than one point
Products of hereditarily indecomposable continua are 2-connected
Products of threads.
Products with non-linear finite-set-aposyndetic continua
Property of being semi-Kelley for the cartesian products and hyperspaces
In this paper we construct a Kelley continuum such that is not semi-Kelley, this answers a question posed by J.J. Charatonik and W.J. Charatonik in A weaker form of the property of Kelley, Topology Proc. 23 (1998), 69–99. In addition, we show that the hyperspace is not semi- Kelley. Further we show that small Whitney levels in are not semi-Kelley, answering a question posed by A. Illanes in Problemas propuestos para el taller de Teoría de continuos y sus hiperespacios, Queretaro, 2013.
Pseudo-homotopies of the pseudo-arc
Let be a continuum. Two maps are said to be pseudo-homotopic provided that there exist a continuum , points and a continuous function such that for each , and . In this paper we prove that if is the pseudo-arc, is one-to-one and is pseudo-homotopic to , then . This theorem generalizes previous results by W. Lewis and M. Sobolewski.