Compactness in the First Baire Class and Baire-1 Operators

For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset of B1 (M, E) is relatively compact, etc. We also show that our class includes Gulko compact. In the second part of the paper we examine under which conditions a bounded linear operator T : X ∗ → Y so that T |BX ∗ : (BX ∗ , w∗ ) → Y is a Baire-1 function, is a pointwise limit of a sequence (Tn ) of operators with T |BX ∗ : (BX ∗ , w∗ ) → (Y, · ) continuous for all n ∈ N. Our results in this case are connected with classical results of Choquet, Odell and Rosenthal.

Information Technologies for the Preservation of Language Heritage

In this paper we try to present how information technologies as tools for the creation of digital bilingual dictionaries can help the preservation of natural languages. Natural languages are an outstanding part of human cultural values and for that reason they should be preserved as part of the world cultural heritage. We describe our work on the bilingual lexical database supporting the Bulgarian-Polish Online dictionary. The main software tools for the web- presentation of the dictionary are shortly described. We focus our special attention on the presentation of verbs, the richest from a specific characteristics viewpoint linguistic category in Bulgarian.

Language Resources – a Part of World Cultural Heritage

This article briefly reviews multilingual language resources for Bulgarian, developed in the frame of some international projects: the first-ever annotated Bulgarian MTE digital lexical resources, Bulgarian-Polish corpus, Bulgarian-Slovak parallel and aligned corpus, and Bulgarian-Polish-Lithuanian corpus. These resources are valuable multilingual dataset for language engineering research and development for Bulgarian language. The multilingual corpora are large repositories of language data with an important role in preserving and supporting the world's cultural heritage, because the natural language is an outstanding part of the human cultural values and collective memory, and a bridge between cultures.

Online Dictionary - Tool for Preservation of Language Heritage

The paper aims to represent a bilingual online dictionary as a useful tool helping preservation of the natural languages. The author focuses on the approach that was taken to develop compatible bilingual lexical database for the Bulgarian-Polish online dictionary. A formal model for the dictionary encoding is developed in accordance with the complex structures of the dictionary entries. These structures vary depending on the grammatical characteristics of Bulgarian headwords. The Web-application for presentation of the bilingual dictionary is also describred.