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On the lp-equivalence of ultrafilters

Baars Jan

Bulletin of the Polish Academy of Sciences. Mathematics

2022

Vol. 70, no. 1

63--82

We show for n,m≥1 and {u1,…,un,v1,…,vm}⊆ω∗ that Cp(⨁ni=1ωui) and Cp(⨁mi=1ωvi) are linearly homeomorphic if and only if n=m and there is a permutation π:{1,…,n}→{1,…,n} such that for every i≤n, ωui and ωvπ(i) are homeomorphic. This generalizes a result by Gul'ko. We will also show that for n,m≥1, {u1,…,un}⊆ω∗ and countable spaces Y1,…,Yn with only one non-isolated point, if Cp(⨁ni=1ωui) and Cp(⨁mi=1Yi) are linearly homeomorphic, then m≤n. Moreover, m=n if and only if each Yi is homeomorphic to ωvi for some vi∈ω∗.https://www.msn.com/pl-pl/feed