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Scientific Seminar:

Topological Algebra
Founded by Igor Guran & Oleg Gutik in 2007

Speaker: Oleksandra Sobol


Semigroups with strongly tight ideal series and their $\mathcal{I}_\lambda^n$-extensions, II

When & where: May 15, 2019, at 1505 at Room 372

In the paper [O. Gutik, J. Lawson, and D. Repovš, Semigroup closures of finite rank symmetric inverse semigroups, Semigroup Forum 78 (2009), no. 2, 326-336 (doi: 10.1007/s00233-008-9112-2, 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)


Hemi-metrizable spaces and an analogue of Kenderov's and Debs' theorems

When & where: May 15, 2019, at 1640 at Room 372

A function d:X × X → [0;+∞) calls hemi-metric 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 hemi-metrizable if there exist a hemi-metric d such that the topology of X is generated by the base consisting of open balls Bd(a,r)={x∈X: d(x,a)< r}. We prove that every hemi-metrizable T1-space which is β-σ-unfavorable for the Christensen game has a metrizable dense Gδ-subspace. On the other hand we give an example of a normal Baire hereditarily separable space Lindelöf space which is hemi-metrizable but β-σ-favorable for the Saint-Raymond game.

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