33 citations · 687 across the 231 of their papers we have counts for
16 papers · 1 filter
Scattered Subsets of Groups
T. O. Banakh, I. V. Protasov, S. V. Slobodianiuk
We define the scattered subsets of a group as asymptotic counterparts of scattered subspaces of a topological space, and prove that a subset of a group is scattered if and…
Extremal densities and measures on groups and -spaces and their combinatorial applications
Taras Banakh
This text contains lecture notes of the course taught to Ph.D. students of Jagiellonian University in Krakow on 25-28 November, 2013.
-spaces
Taras Banakh
A regular topological space is defined to be a -space if it has countable Pytkeev network. A network for is called a Pytkeev network if for any…
On critical cardinalities related to -sets
Taras Banakh, Michal Machura, Lubomyr Zdomskyy
In this note we collect some known information and prove new results about the small uncountable cardinal . The cardinal is defined as the smallest c…
On linear topological spaces (linearly) homeomorphic to
Taras Banakh
We prove that every infinite-dimensional (locally convex) linear topological space that can be expressed as a direct limit of finite-dimensional metrizable compacta is (linearly) h…
Micro and Macro Fractals generated by multi-valued dynamical systems
Taras Banakh, Natalia Novosad
Given a multi-valued function on a topological space we study the properties of its fixed fractal, which is defined as the closure of the orbit $Φ^ω(Fix(Φ))=\bigcup_{n\inω}…