Displaying similar documents to “DMF-algebras: representation and topological characterization”

Description of quotient algebras in function algebras containing continuous unbounded functions

Mati Abel, Jorma Arhippainen, Jukka Kauppi (2012)

Open Mathematics

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Let X be a completely regular Hausdorff space, 𝔖 a cover of X, and C b ( X , 𝕂 ; 𝔖 ) the algebra of all 𝕂 -valued continuous functions on X which are bounded on every S ∈ 𝔖 . A description of quotient algebras of C b ( X , 𝕂 ; 𝔖 ) is given with respect to the topologies of uniform and strict convergence on the elements of 𝔖 .

Condensations of Tychonoff universal topological algebras

Constancio Hernández (2001)

Commentationes Mathematicae Universitatis Carolinae

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Let ( L , 𝒯 ) be a Tychonoff (regular) paratopological group or algebra over a field or ring K or a topological semigroup. If nw ( L , 𝒯 ) ≤ τ and nw ( K ) ≤ τ , then there exists a Tychonoff (regular) topology 𝒯 * ⊆ 𝒯 such that w ( L , 𝒯 * ) ≤ τ and ( L , 𝒯 * ) is a paratopological group, algebra over K or a topological semigroup respectively.

Some applications of the ultrafilter topology on spaces of valuation domains, Part II

Carmelo Antonio Finocchiaro, Marco Fontana (2010)

Actes des rencontres du CIRM

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Let K be a field and A be a subring of K . In the present note, we present the main applications of the so called on the space Zar ( K | A ) , introduced in the previous Part I. After recalling that Zar ( K | A ) is a spectral space, we give an explicit description of Zar ( K | A ) as the prime spectrum of a ring (even in the case when the quotient field of A is a proper subfield of K ). Moreover, we provide applications of the topological material previously introduced to the study of representations of integrally closed...

𝒵 -distributive function lattices

Marcel Erné (2013)

Mathematica Bohemica

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It is known that for a nonempty topological space X and a nonsingleton complete lattice Y endowed with the Scott topology, the partially ordered set [ X , Y ] of all continuous functions from X into Y is a continuous lattice if and only if both Y and the open set lattice 𝒪 X are continuous lattices. This result extends to certain classes of 𝒵 -distributive lattices, where 𝒵 is a subset system replacing the system 𝒟 of all directed subsets (for which the 𝒟 -distributive complete lattices are just...