К сожалению данный раздел пока представлен только в английском варианте.

Speaking on work I mean all accessible to me kinds of activity and its results, namely the following ones: housework , handiwork , gardening , all kinds of self-perfection , scientific work , teaching , publications , public activity .

Scientific work

    The first of my scientific work published in 1949 had been written as diploma paper in 1947, i.e., more than fifty years ago. This paper was devoted to investigation of some special properties of poiihedra. The subsequent work dealt with geometric topology too, namely with non-trivial imbeddings of zero-dimensional compacts into euclidean spaces (generalization of Antoin's example). Several years I took up different applications .
    I like to search new ideas having no analogue, to create on their basis original scientific theories with minimal restrictions concerning basic notions. Such approach allows us to understand the corresponding significance of either restriction. For example, the extension theory had been constructed for arbitrary topological spaces with no separation axiom, the same approach took place for extension structures. Here the following structures are meant: topological structures , proximity relations , contiguity relations , uniform structures . These directions of investigations always were attracting and are attracting my attention. Here new theories were created.

    The fixed point theory was also very interesting for me, especially the fixed point theory of metric space mappings. There are many publications of different kind , which I prepared on this subjects. One of such publications, which combines a surway of the theory with an account of new results, is rather characteristic for me. I like such construction of papers and often use one. The fact is that such form of paper allow to make clear the place, which any new result takes up in the whole theory.

    Categorical approach also helps to understand the main point. All my publications on category theory had just such purpose, for example the concept of enrichments of categories unites the categories of topological spaces, proximity space, contiguity spaces and uniform spaces. Some results on category theory I included in non-categorical papers. It concerns, of course, the so-called topological type structures and categories of topological type spaces, first of all the category of bitopological spaces , the category of settopological spaces and the category of ratio spaces , only bitopological spaces having been studied systematically.

    There are vast literature devoted to bitopological spaces. The notion of bitopological space in initial variant was understood as a set with two topologies given on this set. The theory of bitopological spaces in such understanding (classical theory) consists of generalization of the usual theory of topological spaces on bitopological spaces, i.e., in passing from one topology given on a set to two topologies --rather trivial approach. The general theory of bitopological spaces created in my papers deals with perfectly new notions having no analogue in topological theory. It proved to be that this theory has interesting applications to topology and algebra. I mean bitopological representations of classes of continuous mappings of topological spaces, bitopological manifolds , bitopological groups .

    Lately a very interesting theory was initiated, namely the so-called duality theory of topologies on products and ratios, This theory gives us, in particular, a possibility of joint study of bitopological, settopological and ratio spaces. Now, I am going to study more systematically the theory of space structures. As the result of this work a book "Space structures, theory and applications" will be written.



    The first of my papers had been published in 1949, i.e., more than fifty years ago. It was a student work. Almost all my papers were published in the four kinds of editions, namely in LOMI (POMI) preprints, in Zapiski Nauchn.Semin LOMI (POMI), in journals , in theses (abstracts) of conferences (symposia) .
    I prefer publications of a big size. Such publication allows to combine a survey with a presentation of new results. It, in turn, not only allows to describe new facts but, besides, points out their role in the whole theory. That is why the total amount of pages of my papers in Zapiski... is considerably more then in the other editions.