Isomorphic C(K) spaces from Almost Disjoint families
- Speaker(s)
- Luis David Reyes Saenz
- Affiliation
- National Autonomous University of Mexico
- Language of the talk
- English
- Date
- June 4, 2025, 4:15 p.m.
- Room
- room 5050
- Seminar
- Topology and Set Theory Seminar
The construction of the Alexandrov-Urysohn (AU) compacta out of Almost Disjoint (AD) families, as well as the space of continuos functions over these compacta, have been intensively studied in recent years. In the present talk I will present some new results and generalize old ones.
In particular, I will focus on three theorems:
- Under MA(sigma-centered) any two AD families of size kappa less than continuous have isomorphic C(K) spaces.
- If the trees defining two AD families are homeomorphic as subspaces of the Baire space then their C(K) spaces are isomorphic.
- The AD families defined by 2^N and 3^N have non-homeomorphic AU compacta.
If time allows I will explain how these techniques can also be applied to other spaces defined from AD families.This extends know results of Hector Alonzo Barriga-Acosta and Fernando Hernandez-Hernandez, c-Many types of a Psi-space, Topology and its Applications, Volume 253, 2019, Pages 1-6.
Witold Marciszewski and Grzegorz Plebanek, Extension operators and twisted sums of c0 and C(K) spaces, Journal of Functional Analysis, Volume 274, Issue 5, 2018, Pages 1491-1529.
Witold Marciszewski and Roman Pol, On Banach spaces whose norm-open sets are Fσ-sets in the weak topology. Journal of Mathematical Analysis and Applications, 350, 2009, 708-722.
This is joint work with Grzegorz Plebanek.