From the 2 of 8 linked papers with an AI index.
8 papers
Approximate homomorphisms on orthomodular lattices
Tomasz Kania
The stability programme initiated by Ulam asks when approximate solutions to algebraic identities must lie near exact ones. For lattices, this leads to the question of when a map t…
Characterising projective and weakly projective Boolean algebras by coherent Freese--Nation separations
Tomasz Kania, Andrzej Kucharski, SÅawomir Turek
The authors define a coherent finite‑separation strengthening of the Freese–Nation property and prove that a Boolean algebra is projective precisely when it has a meet‑closed decom…
Canonical reconstruction and forcing absoluteness of standard structures
Tomasz Kania
The paper identifies a preservation principle that ensures the standard form of various algebraic and topological structures remains absolute between transitive models of set theor…
Halving the original Kalton--Roberts upper bound for nearly additive set functions
Boon Suan Ho, Tomasz Kania
Let denote the optimal Kalton--Roberts constant for approximately additive real-valued set functions on algebras of sets. Kalton and Roberts proved $K_\mathrm{KR}\l…
Finite-codimensional subspaces of Daugavet spaces: projection constants and minimal projections
Tomasz Kania, Grzegorz Lewicki
Over the real or complex field, we establish a duality formula for projection constants of finite-codimensional subspaces of Banach spaces with the Daugavet property. If \[ Y=\bigc…
Semiprojective Banach lattices
Tomasz Kania, Mariusz NiwiÅski
We introduce a norm-controlled notion of semiprojectivity for Banach lattices, requiring liftability of contractive lattice homomorphisms through inductive limits of closed ideals…