*History*

In the history of mathematics, the city of Lviv is known by its mathematical school, which, as a branch of the famous Polish mathematical school was operating mostly between two World Wars.

This comparatevely short period of time was highly productive, in particular, for the development of topology in Lviv due to the contribution of several brilliant Polish topologists such as Waclaw Sierpiriski, Kazimierz Kuratowski, Zygmunt Janiszewski, Bronistaw Knaster, Juliusz P. Schauder. To a great extent, the activity of the Lviv mathematical school was interrupted by the dramatic events of the WWII, which changed the whole infrastructure of the mathematical science in Lviv. This historic period marked the end of the Lviv phenomenon as a branch of Polish mathematical school and also a point of discontinuity of topological investigations in Lviv (perhaps the only topologist working in Lviv during the post-war years was Myron Zaryts'kyi (Zarycki); some of his results concerning operations on sets in topological spaces were cited in "Topology" by K. Kuratowski).

Conditionally, the modem period of development of topology in Lviv started with the organization of the topological seminar at the Lviv University. The seminar is held by the Chair of Algebra and Topology of the Department of Mechanics and Mathematics. The Chair and the seminar were founded in early 80s of the last century and the participants of the seminar are closely related to the Moscow topological school (they are either immediate or intermediate disciples of Moscow topologists from the Chair of General Topology and Geometry at the Moscow State University; see Vol. 107 (1-2) (2000) of Topology and its Applications dedicated to 15th anniversary of this Chair).

The group of topologists at Lviv University carries out research in different areas of topology and related mathematical disciplines: topological algebra (the theory of topological groups and semigroups), categorical topology, dimension theory, in particular, infinite-dimensional topology and topology of infinite-dimensional manifolds, geometric topology, group actions, knot theory, and topology of dynamic systems. Many results are obtained in cooperation with mathematicians from other countries, in particular, from Russia, Poland, Canada, the USA, France, Japan.

During these two decades, the topological seminar became one of the centers around which topological life in Ukraine was concentrated.

M.Zarichnyi