scholarly journals SIMULTANEOUS EXTENSION OPERATORS FOR THE DENSITY TOPOLOGY

1999 ◽  
Vol 25 (1) ◽  
pp. 223
Author(s):  
Kolář
Keyword(s):  
Density Topology ◽  
Simultaneous Extension

A Continuous Extension Operator for Convex Metrics

2010 ◽  
Vol 53 (4) ◽  
pp. 719-729
Author(s):  
I. Stasyuk ◽  
E. D. Tymchatyn
Keyword(s):  
Continuous Extension ◽  
Extension Operator ◽  
Uniform Topology ◽  
Simultaneous Extension ◽  
Peano Continuum ◽  
Convex Metrics

AbstractWe consider the problem of simultaneous extension of continuous convex metrics defined on subcontinua of a Peano continuum. We prove that there is an extension operator for convex metrics that is continuous with respect to the uniform topology.

scholarly journals Quasiconvexity and Density Topology

2014 ◽  
Vol 57 (1) ◽  
pp. 178-187 ◽  
Author(s):  
Patrick J. Rabier
Keyword(s):  
Open Subset ◽  
Measure Zero ◽  
Quasiconvex Functions ◽  
Density Topology ◽  
Approximate Continuity ◽  
The Common

AbstractWe prove that if f : ℝN → ℝ̄ is quasiconvex and U ⊂ ℝN is open in the density topology, then supU ƒ = ess supU f ; while infU ƒ = ess supU ƒ if and only if the equality holds when U = RN: The first (second) property is typical of lsc (usc) functions, and, even when U is an ordinary open subset, there seems to be no record that they both hold for all quasiconvex functions.This property ensures that the pointwise extrema of f on any nonempty density open subset can be arbitrarily closely approximated by values of ƒ achieved on “large” subsets, which may be of relevance in a variety of situations. To support this claim, we use it to characterize the common points of continuity, or approximate continuity, of two quasiconvex functions that coincide away from a set of measure zero.

scholarly journals Normal subspaces of the density topology

1978 ◽  
Vol 75 (2) ◽  
pp. 579-588 ◽  
Author(s):  
Franklin Tall
Keyword(s):  
Density Topology

scholarly journals Density topology and pointwise convergence

2003 ◽  
Vol 4 (2) ◽  
pp. 509 ◽  
Author(s):  
Wladyslaw Wilczynski
Keyword(s):  
Pointwise Convergence ◽  
Continuous Functions ◽  
Density Topology ◽  
Topology Of Pointwise Convergence

<p>We shall show that the space of all approximately continuous functions with the topology of pointwise convergence is not homeomorphic to its category analogue.</p>

scholarly journals A generalization of the c-density topology

2015 ◽  
Vol 62 (1) ◽  
pp. 67-87
Author(s):  
Wojciech Wojdowski
Keyword(s):  
Density Topology ◽  
Basic Properties

Abstract We present a generalization of the Tc -density topology introduced in [WO5] as a topology involving both category and measure approach to the notion of density. We construct an ascending sequence of density topologies which leads to -density topology including all previous topologies. We examine several basic properties of the topologies.

Study on Lightweight of the Engine Piston Based on Topology Optimization

2011 ◽  
Vol 201-203 ◽  
pp. 1308-1311 ◽  
Author(s):  
Fa Rong Du ◽  
Zhi Tao
Keyword(s):  
Topology Optimization ◽  
High Speed ◽  
Gasoline Engine ◽  
Optimization Method ◽  
Variable Density ◽  
Complex Stress ◽  
Density Topology ◽  
Before And After ◽  
Calculation Results ◽  
Hyper Works

The topology optimization and analysis were studied on the area of piston pin boss for a high-speed gasoline engine based on the variable density topology optimization method. Firstly, the model of the variable density topology optimization was founded. Then, the topology optimization and topology deconstruction on the piston pin boss were carried out by using Hyper Works. In this process, the minimum mass of piston was pursued as an objective function and the displacements of specified nodes on the piston skirt were made as constraints. Based on the topology optimization, the piston configuration of curved rod frame was designed. The complex stress of the piston before and after optimization was calculated respectively by ANSYS. The calculation results indicate that the piston mass can be lightened by 30% through optimizing under the same level of maximal stress, with satisfying the strength requirements. Therefore, the aim of piston lightweight is achieved, and there is no stress concentration in the area of the optimizing piston pin boss, which is propitious to the deformation compatibility of the piston pin boss.

DENSITY TOPOLOGY INVOLVING MEASURE AND CATEGORY

1989 ◽  
Vol 22 (3) ◽  
Author(s):  
Wojciech Wojdowski
Keyword(s):  
Density Topology

scholarly journals A NOTE ON SOME TOPOLOGICAL PROPERTIES OF SETS WITH FINITE PERIMETER

2015 ◽  
Vol 58 (3) ◽  
pp. 637-647 ◽  
Author(s):  
SILVANO DELLADIO
Keyword(s):  
Topological Properties ◽  
Density Topology ◽  
Finite Perimeter

AbstractSome well-known results about the 2-density topology on ${\mathcal R}$ (in particular in the context of the Lusin–Menchoff property) are extended to τbm, i.e. the m-density topology on ${\mathcal R}$n with m ∈ (n,+∞). Every set of finite perimeter in ${\mathcal R}$n is equivalent (in measure) to a set in τbm0, where m0=n+1+${1\over n-1}$. There exists a set of finite perimeter in ${\mathcal R}$n which is not equivalent (in measure) to any member in the a.e.-modification of τbm, whatever m ∈ [n,+∞).

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