The semigroup of increasing functions on the rational numbers has a unique Polish topology
Rings and Algebras
2023-08-15 v2 General Topology
Abstract
The set of increasing functions on the rational numbers, equipped with the composition operation, naturally forms a topological semigroup with respect to the topology of pointwise convergence in which a sequence of increasing functions converges if and only if it is eventually constant at every argument. We develop new techniques to prove there is no other Polish topology turning this semigroup into a topological one, and show that previous techniques are insufficient for this matter.
Keywords
Cite
@article{arxiv.2305.04921,
title = {The semigroup of increasing functions on the rational numbers has a unique Polish topology},
author = {Michael Pinsker and Clemens Schindler},
journal= {arXiv preprint arXiv:2305.04921},
year = {2023}
}
Comments
43 pages, 7 figures