Let Ω be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by H(Ω) the Banach algebra of all bounded holomorphic functions on Ω, with pointwise operations and the supremum norm. We show that the topological stable rank of H(Ω) is equal to 2. The proof is based on Suarez’s theorem that the topological stable rank of H(D) is equal to 2, where D is t...

— Let Ω be a circular domain, that is, an open disk with finitely many closed disjoint disks removed. Denote by H(Ω) the Banach algebra of all bounded holomorphic functions on Ω, with pointwise operations and the supremum norm. We show that the topological stable rank of H(Ω) is equal to 2. The proof is based on Suarez’s theorem that the topological stable rank of H(D) is equal to 2, where D is...

Abstract This paper is a contribution to understanding what properties should topological algebra on Stone space satisfy be profinite. We reformulate and simplify proofs for some known using syntactic congruences. also clarify the role of various alternative ways describing congruences, namely by finite sets terms compact continuous self mappings algebra.

The concept of a topology for the fundamental group appears to have originated with Hurewicz (1935), but it has been actively studied only for the last ten years. The classical fundamental group of a pointed topological space X naturally inherits the quotient topology from the space of based loops in X endowed with the compact-open topology. The resulting space, called the topological fundament...

We compare how computational effects are modelled in Classical Domain Theory and Topological Domain Theory. Both of these theories provide powerful toolkits for denotational semantics: Classical Domain Theory being introduced by Scott, and well-established and developed since; Topological Domain Theory being a generalization in which topologies more general than the Scott-topology are admitted....

We survey the present trends in theory of universal arrows to forgetful functors from various categories of topological algebra and functional analysis to categories of topology and topological algebra. Among them are free topological groups, free locally convex spaces, free Banach-Lie algebras, and more. An accent is put on relationship of those constructions with other areas of mathematics an...