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 groups. Our approach uses only elementary ...

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 groups. Our approach uses only elementar...

Using locally convex functions, we show that the dual of the segment Voronoi diagram in the plane can be computed by a flip algorithm.

‎‎‎in this paper‎, ‎the‎ notion of injectivity with respect to order dense embeddings in ‎‎the category of $s$-posets‎, ‎posets with a monotone action of a‎ pomonoid $s$ on them‎, ‎is studied‎. ‎we give a criterion‎, ‎like the baer condition for injectivity of modules‎, ‎or skornjakov criterion for injectivity of $s$-sets‎, ‎for the order dense injectivity‎. ‎also‎, ‎we consider such injectivit...

A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ point-wise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ point-wise. An extension $Y$ ...

In Chapter 1, we introduce a notion of universality for subgroups of Polish groups that has both algebraic and topological aspects. More precisely, given a class C of subgroups of a topological group Γ, we say that a subgroup H ∈ C is a universal C subgroup of Γ if every subgroup K ∈ C is a continuous homomorphic preimage of H. Such subgroups may be regarded as complete members of C with respec...

Abstract We prove that certain families of homogenous affine iterated function systems in $\mathbb {R}^{d}$ have the property open set condition and existence exact overlaps both occur densely space translation parameters. These examples demonstrate theorems Falconer Jordan–Pollicott–Simon on almost sure dimensions self-affine sets measures, exceptional parameters can be a dense set. The proof ...

For a function defined on a convex set in a Euclidean space, midpoint convexity is the property requiring that the value of the function at the midpoint of any line segment is not greater than the average of its values at the endpoints of the line segment. Midpoint convexity is a well-known characterization of ordinary convexity under very mild assumptions. For a function defined on the integer...

BACKGROUND Cardiovascular magnetic resonance using displacement encoding with stimulated echoes (DENSE) is capable of assessing advanced measures of cardiac mechanics such as strain and torsion. A potential hurdle to widespread clinical adoption of DENSE is the time required to manually segment the myocardium during post-processing of the images. To overcome this hurdle, we proposed a radical a...

OBJECTIVE In this paper we present our observation of a specific sign on transvaginal ultrasound that may help basic minimal invasive surgeons diagnose vesico-uterine adhesions preoperatively. METHODS The ultrasound images of the latest eleven patients who were preoperatively diagnosed with vesico-uterine adhesions using transvaginal ultrasound were compared with their intraoperative findings...