||In this paper we introduce and study a new topologo-algebraic structure called a (di)topological unosemigroup. This is a topological semigroup endowed with continuous unary operations of left and right units (which have certain continuous division property called the dicontinuity). We show that the class of ditopological unosemigroups contains all topological groups,
all topological semilattices, all uniformizable topological unosemigroups, all compact topological unosemigroups, and is closed under the operations of taking subunosemigroups, Tychonoff
product, reduced product, semidirect product, and the Hartman-Mycielski extension.|
1. T. Banakh, O. Hryniv, On closed embeddings of free topological algebras, Visnyk Lviv Univ., 61 (2003),
21–25; available at http://arxiv.org/abs/1202.4480.|
2. T. Banakh, I. Pastukhova, Embedding ditopological inverse semigroups into the products of cones over
3. R. Brown, S. Morris, Embeddings in contractible or compact objects, Colloq. Math., 38 (1977/78), ¹2,
4. J.H. Carruth, J.A. Hildebrant, R.J. Koch, The Theory of Topological Semigroups, II. Marcell Dekker,
Inc., New York and Basel, 1986.
5. J. Desharnais, P. Jipsen, G. Struth, Domain and antidomain semigroups, in: Relations and Kleene algebra
in computer science, 73–87, Lecture Notes in Comput. Sci., Springer, Berlin, 2009.
6. S. Hartman, J. Mycielski, On the embedding of topological groups into connected topological groups, Colloq.
Math., 5 (1958), 167–169.
7. O. Hryniv, Universal objects in some classes of Clifford topological inverse semigroups, Semigroup Forum,
75 (2007), ¹3, 683–689.