Search results for "Connected space"
showing 10 items of 35 documents
Pseudo-path connected homogeneous continua
2015
Abstract The main result of this paper states that every homogeneous pseudo-path connected continuum is weakly chainable, or equivalently, every homogeneous continuum connected by continuous images of the pseudo-arc is itself a continuous image of the pseudo-arc. We notice that even though there exist homogeneous path connected continua that are not continuous images of an arc (Prajs, 2002), they all are continuous images of the pseudo-arc.
A double mean field equation related to a curvature prescription problem
2019
We study a double mean field-type PDE related to a prescribed curvature problem on compacts surfaces with boundary. We provide a general blow-up analysis, then a Moser-Trudinger inequality, which gives energy-minimizing solutions for some range of parameters. Finally, we provide existence of min-max solutions for a wider range of parameters, which is dense in the plane if $��$ is not simply connected.
Generalized John disks
2014
Abstract We establish the basic properties of the class of generalized simply connected John domains.
Old and New on the Quasihyperbolic Metric
1998
Let D be a proper subdomain of \( {\mathbb{R}^d}\). Following Gehring and Palka [GP] we define the quasihyperbolic distance between a pair x 1, x 2 of points in D as the infimum of \( {\smallint _\gamma }\frac{{ds}}{{D\left( {x,\partial D} \right)}}\) over all rectifiable curves γ joining x 1, x 2 in D. We denote the quasihyperbolic distance between x 1, x 2 by k D (x 1, x 2). As pointed out by Gehring and Osgood [GO], x 1 and x 2 can be joined by a quasihyperbolic geodesic; also see [Mr]. The quasihyperbolic metric is comparable to the usual hyperbolic metric in a simply connected plane domain by the Koebe distortion theorem. For a multiply connected plane domain D these two metrics are co…
Hausdorff measures, Hölder continuous maps and self-similar fractals
1993
Let f: A → ℝn be Hölder continuous with exponent α, 0 < α ≼ 1, where A ⊂ ℝm has finite m-dimensional Lebesgue measure. Then, as is easy to see and well-known, the s-dimensional Hausdorif measure HS(fA) is finite for s = m/α. Many fractal-type sets fA also have positive Hs measure. This is so for example if m = 1 and f is a natural parametrization of the Koch snow flake curve in ℝ2. Then s = log 4/log 3 and α = log 3/log 4. In this paper we study the question of what s-dimensional sets in can intersect some image fA in a set of positive Hs measure where A ⊂ ℝm and f: A → ℝn is (m/s)-Hölder continuous. In Theorem 3·3 we give a general density result for such Holder surfacesfA which implies…
Mean ergodicity of weighted composition operators on spaces of holomorphic functions
2016
[EN] Let phi be a self-map of the unit disc D of the complex plane C and let psi be a holomorphic function on D. We investigate the mean ergodicity and power boundedness of the weighted composition operator C-phi,C-psi(f) = psi(f o phi) with symbol phi and multiplier psi on the space H(D). We obtain necessary and sufficient conditions on the symbol phi and on the multiplier psi which characterize when the weighted composition operator is power bounded and (uniformly) mean ergodic. One necessary condition is that the symbol phi has a fixed point in D. If phi is not a rational rotation, the sufficient conditions are related to the modulus of the multiplier on the fixed point of phi. Some of o…
A remark on weakly convex continuous mappings in topological linear spaces
2009
Abstract Let C be a compact convex subset of a Hausdorff topological linear space and T : C → C a continuous mapping. We characterize those mappings T for which T ( C ) is convexly totally bounded.
A non-g-contractible uniformly path connected continuum
1999
Abstract An example of a uniformly path connected, plane continuum P is constructed and proved to admit no continuous surjection onto P homotopic to the constant map. This answers a question of D.P. Bellamy in the negative.
On fuzzification of topological categories
2014
This paper shows that (L,M)-fuzzy topology of U. Hohle, T. Kubiak and A. Sostak is an instance of a general fuzzification procedure for topological categories, which amounts to the construction of a new topological category from a given one. This fuzzification procedure motivates a partial dualization of the machinery of tower extension of topological constructs of D. Zhang, thereby providing the procedure of tower extension of topological categories. With the help of this dualization, we arrive at the meta-mathematical result that the concept of (L,M)-fuzzy topology and the notion of approach space of R. Lowen are ''dual'' to each other.
TOPOLOGICAL PARTIAL *-ALGEBRAS: BASIC PROPERTIES AND EXAMPLES
1999
Let [Formula: see text] be a partial *-algebra endowed with a topology τ that makes it into a locally convex topological vector space [Formula: see text]. Then [Formula: see text] is called a topological partial *-algebra if it satisfies a number of conditions, which all amount to require that the topology τ fits with the multiplier structure of [Formula: see text]. Besides the obvious cases of topological quasi *-algebras and CQ*-algebras, we examine several classes of potential topological partial *-algebras, either function spaces (lattices of Lp spaces on [0, 1] or on ℝ, amalgam spaces), or partial *-algebras of operators (operators on a partial inner product space, O*-algebras).