We shall discuss recent results on complete semitopological semilattices and an interplay between completeness and absolute H-closedness. Some open problems will be posed.

We survey the functorial dependence between various geometry categories: topology, uniform topology, asymptology, bornologies, function algebras, compactifications, group algebras.

Розглядаються розширення динамічних схем Вороного. Наведено авлгоритми та приклади у випадку n=4.

We discuss on the results of the paper: Bing Yao, Meimei Zhao, Xiaohui Zhang, Yarong Mu, Yirong Sun, Mingjun Zhang, Sihua Yang, Fei Ma, Jing Su, Xiaomin Wang, Hongyu Wang, Hui Sun, Topological coding and topological matrices toward network overall security, arXiv:1909.01587.

We discuss on the results of the paper: Bing Yao, Meimei Zhao, Xiaohui Zhang, Yarong Mu, Yirong Sun, Mingjun Zhang, Sihua Yang, Fei Ma, Jing Su, Xiaomin Wang, Hongyu Wang, Hui Sun, Topological coding and topological matrices toward network overall security, arXiv:1909.01587.

We discuss on the results of the paper: Bing Yao, Meimei Zhao, Xiaohui Zhang, Yarong Mu, Yirong Sun, Mingjun Zhang, Sihua Yang, Fei Ma, Jing Su, Xiaomin Wang, Hongyu Wang, Hui Sun, Topological coding and topological matrices toward network overall security, arXiv:1909.01587.

We discuss on structure of the semilattice of topologies on an infinite semigroup of $\lambda\times\lambda$-matrix units $B_\lambda$. In particular minimal semigroup topologies on $B_\lambda$ will be described.

We discuss on structure of the semilattice of topologies on an infinite semigroup of $\lambda\times\lambda$-matrix units $B_\lambda$. In particular minimal semigroup topologies on $B_\lambda$ will be described.

For each cardinal $\kappa$ we construct an infinite $\kappa$-bounded (and hence countably compact) regular space $R_{\kappa}$ such that for any $T_1$ space $Y$ of pseudo-character $\leq\kappa$, each continuous function $f:R_{\kappa}\rightarrow Y$ is constant. This result resolves two problems posted by Tzannes in Open Problems from Topology Proceedings [E. Pearl, Problems from Topology Proceedings, Topology Atlas, Toronto, 2003] and extends results of Ciesielski and Wojciechowski [K.C. Ciesielski and J. Wojciechowski, Cardinality of regular spaces admitting only constant continuous functions, Topology Proceedings, 47 (2016), 313-329.] and Herrlich [H. Herrlich, Wann sind alle stetigen, Abbildungen in $Y$ Konstant? Math. Z. 90 (1965), 152-154].
This is joint work with Alexander Osipov.

For each cardinal $\kappa$ we construct an infinite $\kappa$-bounded (and hence countably compact) regular space $R_{\kappa}$ such that for any $T_1$ space $Y$ of pseudo-character $\leq\kappa$, each continuous function $f:R_{\kappa}\rightarrow Y$ is constant. This result resolves two problems posted by Tzannes in Open Problems from Topology Proceedings [E. Pearl, Problems from Topology Proceedings, Topology Atlas, Toronto, 2003] and extends results of Ciesielski and Wojciechowski [K.C. Ciesielski and J. Wojciechowski, Cardinality of regular spaces admitting only constant continuous functions, Topology Proceedings, 47 (2016), 313-329.] and Herrlich [H. Herrlich, Wann sind alle stetigen, Abbildungen in $Y$ Konstant? Math. Z. 90 (1965), 152-154].
This is joint work with Alexander Osipov.

We discuss on structure of the semilattice of topologies on an infinite semigroup of matrix units. Also, minimal semigroup topologies on such semigroups will be partially described.
This is a continuation of the report on the seminar Topology & Applications

We discuss on embedings of a Taimanov semigroup (see definition: [A.D. Taimanov, An example of a semigroup which admits only the discrete topology, Algebra i Logika 12:1 (1973) 114-116 (in Russian), English transl. in: Algebra and Logic 12:1 (1973), 64-65] or [O. Gutik, Topological properties of Taimanov semigroups, Mathematical Bulletin of the Shevchenko Scientific Society 13 (2016), 29-34 (arXiv:1612.08677]) into compact-like (semi)topological semigroups.

We discuss on structure of the semilattice of topologies on semigroup of matrix units. In particular, we describe all minimal topologies in some class of semigroup topologies on semigroup of matrix units.