5 papers
Embedding for countable into as Besicovitch functions
Jan Dudák
Extending a recent result from [Bull. Belg. Math. Soc. Simon Stevin 33 (2026), 138-144], we prove that the space of continuous functions on any countable compact space a…
Typical dynamics of Newton's method
Jan Dudák, T. H. Steele
This article consists of two papers: by Steele and by Dudák and Steele. L…
Compact spaces homeomorphic to their respective squares
Jan Dudák, Benjamin Vejnar
We deal with topological spaces homeomorphic to their respective squares. Primarily, we investigate the existence of large families of such spaces in some subclasses of compact met…
Borel Measurable Hahn-Mazurkiewicz Theorem
Jan Dudák, Benjamin Vejnar
It is well known due to Hahn and Mazurkiewicz that every Peano continuum is a continuous image of the unit interval. We prove that an assignment, which takes as an input a Peano co…
The complexity of homeomorphism relations on some classes of compacta with bounded topological dimension
Jan Dudák, Benjamin Vejnar
We are dealing with the complexity of the homeomorphism equivalence relation on some classes of metrizable compacta from the viewpoint of invariant descriptive set theory. We prove…