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Scientific Seminar:
Topological Algebra

Speaker: 
Oleksandra Sobol

Talk: 
Semigroups with strongly tight ideal series and their $\mathcal{I}_\lambda^n$extensions, II 
When & where:  May 15, 2019, at 15^{05 } at Room 372 
Abstract: 
In the paper [O. Gutik, J. Lawson, and D. Repovš, Semigroup closures of finite rank symmetric inverse semigroups, Semigroup Forum 78 (2009), no. 2, 326336 (doi: 10.1007/s0023300891122, MR2486644 (2010f:20066), Zbl 1165.22002, arXiv:0804.1439)] the notion of a semigroup which admits a tight ideal series was intruduced. We introduce the notion of a semigroup which admits a stronly tight ideal series and it more cstronger them above. We discuss on property of such semigroups and show that an $\mathcal{I}_\lambda^n$extension preserves this property for any cardinal $\lambda>0$ and any positive integer $n\leqslant\lambda$. 
Speaker: 
Oleksandr Maslyuchenko (University of Silesia in Katowice, Poland)

Talk: 
Hemimetrizable spaces and an analogue of Kenderov's and Debs' theorems 
When & where:  May 15, 2019, at 16^{40 } at Room 372 
Abstract: 
A function d:X × X → [0;+∞) calls hemimetric if d(x,x)=0 and d(x,y) ≤ d(x,z) + d(z,y) for any x,y,z∈X. We call a topological space X hemimetrizable if there exist a hemimetric d such that the topology of X is generated by the base consisting of open balls B_{d(a,r)}={x∈X: d(x,a)< r}. We prove that every hemimetrizable T_{1}space which is βσunfavorable for the Christensen game has a metrizable dense G_{δ}subspace. On the other hand we give an example of a normal Baire hereditarily separable space Lindelöf space which is hemimetrizable but βσfavorable for the SaintRaymond game. 