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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)

- Maria V. Ferrer, Salvador Hernandez, Dmitri Shakhmatov
- ArXiv
- 2013

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)

- Tsugunori NOGURA, Dmitri SHAKHMATOV
- 2007

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)

- Y. A. Shelygin, S. A. Frolov, S. I. Achkasov, O. I. Sushkov, D. G. Shakhmatov
- Techniques in Coloproctology
- 2012

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)

- Iu A Shelygin, S A Frolov, S I Achkasov, O I Sushkov, D G Shakhmatov
- Khirurgiia
- 2012

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)

- Evgeniy Surovegin, S Achkasov, I Lukashevych, D Shakhmatov
- Clinical nutrition ESPEN
- 2016