Prove if s is finite set then s is a convex and compact set

Assignment Help Mathematics

Reference no: EM131330310

1. Prove that if S is a finite set then (S) is a convex and compact set.

2. Let A ⊆ Rⁿ and B ⊆ R^m be two compact sets. Prove that the product set A × B ⊆ R^n+m is a compact set.

3. Let A ⊆ Rⁿ and B ⊆ R^m be two convex sets. Prove that the product set A × B ⊆ R^n+m is a convex set.

Reference no: EM131330310

Questions Cloud

What are the agents in your model : How would you simulate the different policy choices, namely, the allocation of funds to minimize commuter time? What measures would you collect to answer the council ' s question?

Feasibility analysis for application development project : Discuss how your organization selected this project for further consideration. Be sure to include an overview of how decision rights are allocated. Perform a feasibility analysis for this application development project, indicating for each risk:

Approaches-breakdown-workload and incremental : Using the following information, calculate the total salesforce size necessary by using each of the following approaches: breakdown, workload, and incremental. Be sure to show your work. Also, explain the advantages and disadvantages of each approach..

Components of a telecommunication system : Components of a Telecommunication System and Basic Computer Network Components are major components of a business : What are the main differences of these two systems? Do you need to have both of them to support your communication needs? Why or w..

Prove if s is finite set then s is a convex and compact set : Prove that if S is a finite set then (S) is a convex and compact set.- Let A ⊆ R n and B ⊆ R m be two compact sets. Prove that the product set A × B ⊆ R n+m is a compact set.

Composing and using regular expressions : Regular expressions became popular with the introduction of the UNIX operating system in 1960s and its text processing tools such as grep and ed. Write a two to three (2-3) page paper in which you:

How behavior of the modified model differs from the original : Open the NetLogo Flocking model from the Biology section of the models library, which shows emergent rules for generating bird flocks. Can you add a predator bird that changes the other birds ' behavior?

What is the impact on taxes from the sale of the machine : Bill Sharpe, owner of Sharper Knives, Inc is closing his business at the end of the current fiscal year. His sole asset, the knife-sharpening machine, is four years old. A depreciation table for the asset is shown below. Bill has agreed to sell the m..

Working for a company with outdated multimedia tools : You are currently working for a company with outdated multimedia tools. Give proposal to your manager that includes the following:

User Account

All Pages