5 papers
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,…
A nontrivial uniform algebra Dirichlet on its maximal ideal space
Alexander J. Izzo
It is shown that there exists a nontrivial uniform algebra that is Dirichlet on its maximal ideal space and has a dense set of elements that are exponentials. This answers a 65-yea…
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…
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…
A sharper Swiss cheese
Alexander J. Izzo
It is shown that there exists a compact planar set K such that the uniform algebra R(K) is nontrivial and strongly regular. This settles an issue raised by Donald Wilken 55 years a…