Dmitri Shakhmatov

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For an abelian topological group G, let Ĝ denote the dual group of all continuous characters endowed with the compact open topology. Given a closed subset X of an infinite compact abelian group G such that w(X) < w(G), and an open neighbourhood U of 0 in T, we show that |{χ ∈ Ĝ : χ(X) ⊆ U}| = |Ĝ|. (Here, w(G) denotes the weight of G.) A subgroup D of G(More)
Let G be a topological group with the identity element e. Given a space X, we denote by Cp(X,G) the group of all continuous functions from X to G endowed with the topology of pointwise convergence, and we say that X is: (a) G-regular if, for each closed set F ⊆ X and every point x ∈ X \ F , there exist f ∈ Cp(X,G) and g ∈ G \ {e} such that f(x) = g and f(F(More)
Let I be an infinite set, {Gi : i ∈ I} be a family of (topological) groups and G = ∏ i∈I Gi be its direct product. For J ⊆ I , pJ : G → ∏ j∈J Gj denotes the projection. We say that a subgroup H of G is: (i) uniformly controllable in G provided that for every finite set J ⊆ I there exists a finite set K ⊆ I such that pJ (H) = pJ (H ∩ ⊕ i∈K Gi); (ii)(More)
We prove that: (i) a pathwise connected, Hausdorff space which has a continuous selection is homeomorphic to one of the following four spaces: singleton, [0, 1), [0, 1] or the long line L, (ii) a locally connected (Hausdorff) space which has a continuous selection must be orderable, and (iii) an infinite connected, Hausdorff space has exactly two continuous(More)
If a discrete subset S of a topological group G with the identity 1 generates a dense subgroup of G and S∪{1} is closed in G, then S is called a suitable set for G. We apply Michael’s selection theorem to offer a direct, self-contained, purely topological proof of the result of Hofmann and Morris [8] on the existence of suitable sets in locally compact(More)
We give a necessary and sufficient condition, in terms of a certain reflection principle, for every unconditionally closed subset of a group G to be algebraic. As a corollary, we prove that this is always the case when G is a direct product of an Abelian group with a direct product (sometimes also called a direct sum) of a family of countable groups. This(More)
We report a case of sigmoid colon resection by single-incision laparoscopic surgery using transvaginal access. The patient was a 54-year-old woman with early stage sigmoid cancer who had no previous surgery and had a body mass index of 23.5 kg/m2. The operative time was 270 min, and the blood loss was negligible. We used only transvaginal access, since no(More)
The experience of 193 manually assisted laparoscopic operations on the reason of colon cancer was analyzed. The mean age of the patients was 63.6±11.3 years. Men were 85 (44%), women - 108 (56%). The majority of patients had tumor of 2nd or 3rd stage. The mean body mass index was 27.6±4.6 kg/m2. The conversion was needed in 8 (4.1%) cases. There were no(More)
A Hausdorff topological group G is minimal if every continuous isomorphism f : G → H between G and a Hausdorff topological group H is open. Clearly, every compact Hausdorff group is minimal. It is well known that every infinite compact Hausdorff group contains a non-trivial convergent sequence. We extend this result to minimal abelian groups by proving that(More)