Topological Groups - учебный курс | ИСТИНА – Интеллектуальная Система Тематического Исследования НАукометрических данных

Topological Groupsучебный курс

Автор: Сипачева О.В.
Год создания: 2016
Организация: МГУ имени М.В. Ломоносова
Курс на иностранном языке
Описание: Topological space. Separability axioms, normality, compactness-type properties. Continuous maps. Open, closed, and quotient maps, retractions. Topological groups. Algebraic systems with topology consistent with operations. Nontopologizable groups. Sufficent conditions for a group to be topologizable. Topological quotient groups. Topological (Tychonoff) product of topological spaces. Free topological groups. The inductive limit topology and conditions under which the natural multiplication maps in free topological groups are quotient. The ccc property in topological groups. Spaces with continuous Mal'tsev operations. Theorem: any compact space with a continuous Mal'tsev operation is a retract of a topological group. Completeness of free topological groups. Subgroups of free topological groups. Abelian and Boolean free topological groups. Locally convex spaces. Free locally convex spaces. Completeness. Stratifiable spaces. The Borges--Dugundji theorem on an extension operator. Free algebraic systems: Mal'tsev's approach.
Добавил в систему: Сипачева Ольга Викторовна

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