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Classifications and characterizations of Baire-1 functions

Persephone Kiriakouli (1998)

Commentationes Mathematicae Universitatis Carolinae

Kechris and Louveau in [5] classified the bounded Baire-1 functions, which are defined on a compact metric space K , to the subclasses 1 ξ ( K ) , ξ < ω 1 . In [8], for every ordinal ξ < ω 1 we define a new type of convergence for sequences of real-valued functions ( ξ -uniformly pointwise) which is between uniform and pointwise convergence. In this paper using this type of convergence we obtain a classification of pointwise convergent sequences of continuous real-valued functions defined on a compact metric space K , and...

Condensations of Tychonoff universal topological algebras

Constancio Hernández (2001)

Commentationes Mathematicae Universitatis Carolinae

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.

Frame monomorphisms and a feature of the l -group of Baire functions on a topological space

Richard N. Ball, Anthony W. Hager (2013)

Commentationes Mathematicae Universitatis Carolinae

“The kernel functor” W k LFrm from the category W of archimedean lattice-ordered groups with distinguished weak unit onto LFrm, of Lindelöf completely regular frames, preserves and reflects monics. In W , monics are one-to-one, but not necessarily so in LFrm. An embedding ϕ W for which k ϕ is one-to-one is termed kernel-injective, or KI; these are the topic of this paper. The situation is contrasted with kernel-surjective and -preserving (KS and KP). The W -objects every embedding of which is KI are characterized;...

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