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math.CV2025
A nontrivial uniform algebra regular on the Cantor set
J. F. Feinstein, Alexander J. Izzo
We prove the existence of a nontrivial uniform algebra that is logmodular and regular on the Cantor set. As a consequence, we obtain that for every compact metrizable space X witho…
math.GN2025
Approximation by zero-free continuous maps
Alexander J. Izzo
We prove that if E a subset of an n-dimensional manifold, then every continuous R^n-valued map on E that is zero-free on the interior of E can be approximated in the fine topology,…
math.CV2025
Weakly strongly regular uniform algebras
J. F. Feinstein, Alexander J. Izzo
Given a uniform algebra A on a compact Hausdorff space X and a point x in X, denote by M_x the ideal of functions in A that vanish at x and by J_x the ideal of functions in A that…