5 papers · 1 filter
Linear orders on chainable continua
Witold Marciszewski, Julia ÅcisÅowska, Benjamin Vejnar
We define and study certain linear orders on chainable continua. Those orders depend on a sequence of chains obtained from definition of chainability and on a fixed non-principal u…
The converse to Borsuk's result on fans fails
Benjamin Vejnar
A fan is an arc-wise connected hereditarily unicoherent continuum with exactly one branching point. By a result of Borsuk, every fan is a 1-dimensional continuum that can be expres…
The Complexity of Connectedness Relations on Polish Spaces
Michal Hevessy, Yusuf Uyar, Benjamin Vejnar
We systematically investigate three different equivalence relations of connectedness: being connected by arcs, being connected by continua and being connected by chains of continua…
Generically hereditarily equivalent continua and topological characterization of generic maximal chains of generalized Ważewski dendrites
Bryant Rosado Silva, Benjamin Vejnar
The notion of hereditarily equivalent continua is classical in continuum theory with only two known nondegenerate examples (arc, and pseudoarc). In this paper we introduce generica…
Topological fractals revisited
Klára Karasová, Benjamin Vejnar
We prove that every Peano continuum with uncountably many local cut points is a topological fractal. This extends some recent results and it partially answers a conjecture by Hata.…