Sierpi\'nski rank of the Symmetric inverse semigroup
classification
🧮 math.GR
math.RA
keywords
bijectionspartialcompositioncountableeveryobtainedhigginshowie
read the original abstract
We show that every countable set of partial bijections from an infinite set to itself can be obtained as a composition of just two such partial bijections. This strengthens a result by Higgins, Howie, Mitchell and Ru\v{s}kuc stating that every such countable set of partial bijections may be obtained as the composition of two partial bijections and their inverses.
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