Purchase Solution

Lower Hemicontinuity

Not what you're looking for?

Ask Custom Question

Please determine whether or not the 2 correspndences is lower hemicontinuous and please justify why (using definition/proof of lower hemicontinuity):

1)F:R^2->R^2, F(u)={x: x o u =0}

2)F:R^n{0}->R^n, F(x)=B(x;||x||), the closed ball centred at x with radius ||x||.

Thanks
Note: o is the dot product
is the complement
||x|| is the distance

My definiton of lower hemicontinuity is:

F:A->B is a correspondence, A is contained in R^n, B is contained in R^k, p belongs to A. I say that F is lowerhemicontinuous at p if: for all sequences {x^m} in A with x^m->p and for all q belonging to F(p), there exists {y^m} in B with y^m belonging to F(x^m) for all m and y^m->q.

Purchase this Solution
Solution Summary

Lower Hemicontinuity is investigated. The solution is detailed and well presented. The expert examines dot products for complements.

Solution Preview

Please see the attached file for the full solution.
Thanks for using BrainMass.

1. ,
Proof: We consider a sequence and . Then we consider an arbitrary point , then we have . This implies and for some real number . Now we ...

Purchase this Solution
Free BrainMass Quizzes
Transformational Leadership

This quiz covers the topic of transformational leadership. Specifically, this quiz covers the theories proposed by James MacGregor Burns and Bernard Bass. Students familiar with transformational leadership should easily be able to answer the questions detailed below.

Marketing Research and Forecasting

The following quiz will assess your ability to identify steps in the marketing research process. Understanding this information will provide fundamental knowledge related to marketing research.

Accounting: Statement of Cash flows

This quiz tests your knowledge of the components of the statements of cash flows and the methods used to determine cash flows.

Operations Management

This quiz tests a student's knowledge about Operations Management

Academic Reading and Writing: Critical Thinking

Importance of Critical Thinking

View More Free Quizzes
Related BrainMass Solutions

  • Hemicontinuity

    Thanks Note: abs=absolute value is the complement ||x|| is distance My definition of upper hemicontinuity is: F:A->R^k, A contained in R^n, correspondence.

  • Solving for a variable

    38614 Solving for a variable I am trying to solve for P lower squared (lower 2) P lower 1 V lower 1/T lower 1 = P lower 2 V lower 2/T lower 2 see attachment I am trying to solve for P lower squared (lower 2) P lower 1 V lower 1/T lower 1 = P

  • Definite Integral as the Limit of a sum

    Find by the method of summation the value of: (a) ∫ x^3dx, where the lower limit is 0 and the upper limit is 1, i.e., integral of x^3, where the lower limit is 0 and

  • Slack

    Answer: slack on lower path= -1 This solution helps with questions about slacks on the lower path.

  • Lower Specification to Center - Normal Distribution

    Lower specification, LS = 4.0 litre Standard deviation, s = 0.02 % of data below lower specification = 2.5 i.e., probability below lower specification = 0.025 Corresponding Z = -1.96 If center = mu Hence, LS = mu - Z*s => Center = mu = LS

  • Pricing

    A firm might be using a technology, which gives lower cost of production, while others are not able to use it because of certain barriers like copyright, patent. 3. A firm may have lower cost of production because of lower input costs.

  • Convex and lower semi-continuous functions

    So f will be lower semi-continuous as long as it is lower semi-continuous at the origin, the one point we have not yet checked. There are several alternative ways to think about lower semi-continuity.

  • Lower of Cost or Market

    The rule in lower of cost or market (replacement cost) is to use lower of cost or market provided market should not be higher net realizable value (selling price less the cost of disposal) and lower than net realizable value less normal profit margin.

  • Discrimination of families of ferns & lower vascular plants

    127581 Discrimination of Families of Ferns & Lower Vascular Plants What characteristics are used to discriminate among the families of ferns and lower vascular plants?

View More Related Solutions