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math.GN2026
The circle as a topological fractal
Benjamin Vejnar
We prove that no family of two continuous self-maps witnesses that the circle is a topological fractal, answering a question of Karasová and the present author. Since three maps ar…
math.GN2026
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…
math.GN2026
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…