Filip Strobin

Detecting topological and Banach fractals among zero-dimensional spaces

Abstract A topological space X is called a topological fractal if X = ⋃ f ∈ F f ( X ) for a finite system F of continuous self-maps of X, which is topologically contracting in the sense that for every open cover U of X there is a number n ∈ N such that for any functions f 1 , … , f n ∈ F , the set f 1 ∘ … ∘ f n ( X ) is contained in some set U ∈ U . If, in addition, all functions f ∈ F have Lipschitz constant ħ ( X ) is a successor ordinal. For countable compact spaces this classification was recently proved by M. Nowak.

Embedding topological fractals in universal spaces

Let

Attractors of generalized IFSs that are not attractors of IFSs

X

Topological version of generalized (infinite) iterated function systems

be a universal (Urysohn) space. We prove that every topological fractal is homeomorphic (isometric) to the attractor

On a generalization of density topologies on the real line

A_{mathcal F}

On certain uniformly open multilinear mappings

of a function system

Typical behaviour of integrable functions at infinity

{mathcal F}

Spaceability of the set of continuous injections from Bℓp into ℓp with nowhere continuous inverses

on

Uniform openness of multiplication in Banach spaces

X

L_p

consisting of Rakotch contractions.