On closed embeddings of free topological algebras

Let $\mathcal K$ be a complete quasivariety of completely regular universal topological algebras of continuous signature $\mathcal E$ (which means that $\mathcal K$ is closed under taking subalgebras, Cartesian products, and includes all completely regular topological $\mathcal E$-algebras algebraically isomorphic to members of $\mathcal K$). For a topological space $X$ by $F(X)$ we denote the free universal $\mathcal E$-algebra over $X$ in the class $\mathcal K$. Using some extension properties of the Hartman-Mycielski construction we prove that for a closed subspace $X$ of a metrizable (more generally, stratifiable) space $Y$ the induced homomorphism $F(X)\to F(Y)$ between the respective free universal algebras is a closed topological embedding. This generalizes one result of V.Uspenskii concerning embeddings of free topological groups.Comment: 3 page

Metrizability of Clifford topological semigroups

We prove that a topological Clifford semigroup $S$ is metrizable if and only if $S$ is an $M$-space and the set $E=\{e\in S:ee=e\}$ of idempotents of $S$ is a metrizable $G_\delta$-set in $S$. The same metrization criterion holds also for any countably compact Clifford topological semigroup $S$.Comment: 4 page

The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups

In this paper we search for conditions on a countably compact (pseudo-compact) topological semigroup under which: (i) each maximal subgroup $H(e)$ in $S$ is a (closed) topological subgroup in $S$; (ii) the Clifford part $H(S)$(i.e. the union of all maximal subgroups) of the semigroup $S$ is a closed subset in $S$; (iii) the inversion $\operatorname{inv}\colon H(S)\to H(S)$ is continuous; and (iv) the projection $\pi\colon H(S)\to E(S)$, $\pi\colon x\longmapsto xx^{-1}$, onto the subset of idempotents $E(S)$ of $S$, is continuous

Topological monoids of monotone injective partial selfmaps of N\mathbb{N} with cofinite domain and image

In this paper we study the semigroup $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ of partial cofinal monotone bijective transformations of the set of positive integers $\mathbb{N}$. We show that the semigroup $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ has algebraic properties similar to the bicyclic semigroup: it is bisimple and all of its non-trivial group homomorphisms are either isomorphisms or group homomorphisms. We also prove that every locally compact topology $\tau$ on $\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N})$ such that $(\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N}),\tau)$ is a topological inverse semigroup, is discrete. Finally, we describe the closure of $(\mathscr{I}_{\infty}^{\nearrow}(\mathbb{N}),\tau)$ in a topological semigroup

Antimicrobial de-escalation in the critically ill patient and assessment of clinical cure: the DIANA study

Purpose: The DIANA study aimed to evaluate how often antimicrobial de-escalation (ADE) of empirical treatment is performed in the intensive care unit (ICU) and to estimate the effect of ADE on clinical cure on day 7 following treatment initiation. Methods: Adult ICU patients receiving empirical antimicrobial therapy for bacterial infection were studied in a prospective observational study from October 2016 until May 2018. ADE was defined as (1) discontinuation of an antimicrobial in case of empirical combination therapy or (2) replacement of an antimicrobial with the intention to narrow the antimicrobial spectrum, within the first 3 days of therapy. Inverse probability (IP) weighting was used to account for time-varying confounding when estimating the effect of ADE on clinical cure. Results: Overall, 1495 patients from 152 ICUs in 28 countries were studied. Combination therapy was prescribed in 50%, and carbapenems were prescribed in 26% of patients. Empirical therapy underwent ADE, no change and change other than ADE within the first 3 days in 16%, 63% and 22%, respectively. Unadjusted mortality at day 28 was 15.8% in the ADE cohort and 19.4% in patients with no change [p = 0.27; RR 0.83 (95% CI 0.60\u20131.14)]. The IP-weighted relative risk estimate for clinical cure comparing ADE with no-ADE patients (no change or change other than ADE) was 1.37 (95% CI 1.14\u20131.64). Conclusion: ADE was infrequently applied in critically ill-infected patients. The observational effect estimate on clinical cure suggested no deleterious impact of ADE compared to no-ADE. However, residual confounding is likely

Науково-практичний коментар Закону України «Про запобігання корупції» [станом на 1 лип. 2018 р.]

Науково-практичний коментар Закону України «Про запобігання корупції»: станом на 1 лип. 2018 р. / [А. В. Андрєєв, І. Л. Антипова, С. В. Банах та ін.], за заг. ред. Журавльова Д. В. – Київ: Видав. дім «Професіонал», 2018. – 512 с.Коментар розрахований на осіб, уповноважених на виконання функцій держави або місцевого самоврядування та прирівняних до них осіб, які є суб’єктами, на яких поширюється дія Закону України «Про запобігання корупції», на уповноважених осіб, відповідальних за реалізацію антикорупційних програм, суддів, прокурорів, слідчих, детективів, адвокатів, а також на студентів вищих учбових закладів, які готують фахівців в галузі права