Pseudo-Compact Semi-Topological Groups

Митрофан М. Чобан, Петър Ст. Кендеров, Уорън Б. Муурс - Полу-топологична група (съответно, топологична група) е група, снабдена с топология, относно която груповата оперция произведение е частично непрекъсната по всяка от променливите (съответно, непрекъсната по съвкупност от променливите и обратната операция е също непрекъсната). В настоящата работа ние даваме условия, от топологичен характер, една полу-топологична група да е всъщност топологична група. Например, ние показваме, че всяка сепарабелна псевдокомпактна полу-топологична група е топологична група. Показваме също, че всяка локално псевдокомпактна полу-топологична група, чиято групова операция е непрекъсната по съвкупност от променливите е топологична група.

The Interval [0,1] Admits no Functorial Embedding into a Finite-Dimensional or Metrizable Topological Group

An embedding X ⊂ G of a topological space X into a topological group G is called functorial if every homeomorphism of X extends to a continuous group homomorphism of G. It is shown that the interval [0, 1] admits no functorial embedding into a finite-dimensional or metrizable topological group.

Topological Dichotomy and Unconditional Convergence

In this paper, we give a criterion for unconditional convergence with respect to some summability methods, dealing with the topological size of the set of choices of sign providing convergence. We obtain similar results for boundedness. In particular, quasi-sure unconditional convergence implies unconditional convergence.

Isomorphism Problems for the Baire Function Spaces of Topological Spaces

Let a compact Hausdorff space X contain a non-empty perfect subset. If α < β and β is a countable ordinal, then the Banach space Bα (X) of all bounded real-valued functions of Baire class α on X is a proper subspace of the Banach space Bβ (X). In this paper it is shown that: 1. Bα (X) has a representation as C(bα X), where bα X is a compactification of the space P X – the underlying set of X in the Baire topology generated by the Gδ -sets in X. 2. If 1 ≤ α < β ≤ Ω, where Ω is the first uncountable ordinal number, then Bα (X) is uncomplemented as a closed subspace of Bβ (X). These assertions for X = [0, 1] were proved by W. G. Bade [4] and in the case when X contains an uncountable compact metrizable space – by F.K.Dashiell [9]. Our argumentation is one non-metrizable modification of both Bade’s and Dashiell’s methods.

Doitchinov's Construct of Supertopological Spaces is Topological

It is shown that the construct of supertopological spaces and continuous maps is topological.

Regular and Other Kinds of Extensions of Topological Spaces

∗ This work was partially supported by the National Foundation for Scientific Researches at the Bulgarian Ministry of Education and Science under contract no. MM-427/94.

Educational Games for Learning Programming Languages

A concept of educational game for learning programming languages is presented. The idea of learning programming languages and improving programming skills through programming game characters’ behavior is described. The learning course description rules for using in games are suggested. The concept is implemented in a game for learning C# programming language. A common game architecture is modified for using in the educational game. The game engine is built on the base of the graphical engine Ogre3D and extended with game logic. The game has been developed as an industry level commercial product and is planned for sale to educational institutions.

A Software Platform for Educational Board Games

Educational games such as quizzes, quests, puzzles, mazes and logical problems may be modeled as multimedia board games. In the scope of the ADOPTA project1 being under development at the Faculty of Mathematics and Informatics at Sofia University, a formal model for presentation of such educational board games was invented and elaborated. Educational games can be modeled as special board mini-games, with a board of any form and any types of positions. Over defined positions, figures (objects) with certain properties are placed and, next, there are to be defined formal rules for manipulation of these figures and resulted effects. The model has been found to be general enough in order to allow description and execution control of more complex logical problems to be solved by several actions delivered to/by the player according some formal rules and context conditions and, in general, of any learning activities and their workflow. It is used as a base for creation of a software platform providing facilities for easy construction of multimedia board games and their execution. The platform consists of game designer (i.e., a game authoring tool) and game run-time controller communicating each other through game repository. There are created and modeled many examples of educational board games appropriate for didactic purposes, self evaluations, etc., which are supposed to be designed easily by authors with no IT skills and experience. By means of game metadata descriptions, these games are going be included into narrative storyboards and, next, delivered to learners with appropriate profile according their learning style, preferences, etc. Moreover, usage of artificial intelligence agents is planned as well – once as playing virtual opponents of the player or, otherwise, being virtual advisers of the gamer helping him/her in finding the right problem solution within given domain such as discovering a treasure using a location map, finding best tour in a virtual museum, guessing an unknown word in a hangman game, and many others.

About Topological Groups and the Baire Property in Remainders

Александър В. Архангелски, Митрофан М. Чобан, Екатерина П. Михайлова - Изследвани са прирасти със свойството на Бер на топологични групи.

Serious Games in Economics

The European Leonardo da Vinci Transfer of Innovation project “Teacher training to improve attractiveness and quality of management education through the simulation tool ‘Emerald Forest’” which emphases on using the computer simulation tool for increasing attractiveness of teaching and learning in economics is presented in this paper. The observation of using computer systems and especially serious games in education is provided as well. “Education is not the filling of a pail, but the lighting of a fire” - William Butler Yeats

On Local Uniform Topological Algebras

2000 Mathematics Subject Classification: Primary 46H05, 46H20; Secondary 46M20.