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3 results

Conditional mean dimension
Part of
- Spaces with richer structures
BINGBING LIANG
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 10 / October 2022

Published online by Cambridge University Press:

06 September 2021, pp. 3152-3166

Print publication:

October 2022
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We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an extension system. The conditional mean dimension for G-extensions is computed. We also exhibit some applications in dynamical embedding problems.

Finiteness Properties of Some Groups of Local Similarities
Part of
Daniel S. Farley, Bruce Hughes
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 58 / Issue 2 / June 2015

Published online by Cambridge University Press:

10 April 2015, pp. 379-402
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Hughes has defined a class of groups that we call finite similarity structure (FSS) groups. Each FSS group acts on a compact ultrametric space by local similarities. The best-known example is Thompson’s group V. Guided by previous work on Thompson’s group, we show that many FSS groups are of type F∞. This generalizes work of Ken Brown from the 1980s.

Boolean Algebras and Raising Maps to Zero-Dimensional Spaces
Jan van Mill
Journal:

Canadian Mathematical Bulletin / Volume 26 / Issue 1 / 01 March 1983

Published online by Cambridge University Press:

20 November 2018, pp. 70-79

Print publication:

01 March 1983
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Let X be a separable metric space and let be a family of countably many self-maps of X. Then there is a countable subalgebra of the Boolean algebra of regular open subsets of X which is a base for X such that for each the function defined by Φf(B) = (f-1(B))-0 is a homomorphism.