We introduce self-divisible ultrafilters, which we prove to be precisely those w such that the weak congruence relation (w) introduced by. Sobot is an equivalence relation on ss Z. We provide several examples and additional characterisations; notably we show that w is self-divisible if and only if (w) coincides with the strong congruence relation (s) (w), if and only if the quotient (ss Z,circle plus)/(s) (w) is a profinite group. We also construct an ultrafilter w such that (w) fails to be symmetric, and describe the interaction between the aforementioned quotient and the profinite completion (Z) over cap of the integers.
SELF-DIVISIBLE ULTRAFILTERS AND CONGRUENCES IN βZ
Di Nasso, M;Mennuni, R;Pierobon, M;Ragosta, M
2023-01-01
Abstract
We introduce self-divisible ultrafilters, which we prove to be precisely those w such that the weak congruence relation (w) introduced by. Sobot is an equivalence relation on ss Z. We provide several examples and additional characterisations; notably we show that w is self-divisible if and only if (w) coincides with the strong congruence relation (s) (w), if and only if the quotient (ss Z,circle plus)/(s) (w) is a profinite group. We also construct an ultrafilter w such that (w) fails to be symmetric, and describe the interaction between the aforementioned quotient and the profinite completion (Z) over cap of the integers.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
