Essay Available:
Pages:
1 page/β275 words
Sources:
Check Instructions
Style:
APA
Subject:
Mathematics & Economics
Type:
Math Problem
Language:
English (U.S.)
Document:
MS Word
Date:
Total cost:
$ 4.32
Topic:
Proving the Real Variable Theory
Math Problem Instructions:
1.a)Prove that (0, 1) and [0,1) are not compact by constructing an open cover for each that has no finite subcover. (Short – you need only produce the cover, not show it works.). Similarly show that the set [0,1) union (1,2] is not compact.
b)Given S, an arbitrary set of real numbers, and t, an arbitrary limit point of S with t is not in S, construct an open cover of S with no finite subcover. Use the same idea as b, treating “t” in the
same way you dealt with the number 1. This time, do prove that no finite subcover exists.
c) From this, prove that if F is compact, then F must be closed.
d) Prove that if F is compact, then F must be bounded.
Math Problem Sample Content Preview:
Real Variable Theory
Student
Institution
Course
Professor
Date
Real Variable Theory
Question 1a
The main reason the interval is never compact is because it lacks the Heine-borel characteristic. This means that there is a open cover (0,1) that can never be reduced finite subcover.
Un = (an, 2), where an 0
We must define that In = (1/n, 2), which implies that even when we include many In, the interval cannot be covered. This is due to the finite cover that existed. Therefore, the (0,1) and (0,1) are never compact.
When we follow the same method, we can prove that (0,1) and (1,2) is not compact.
Question 1b
Since S is a set of real numbers, t is compact if and only if every individual open...
Get the Whole Paper!
Not exactly what you need?
Do you need a custom essay? Order right now:
π Other Visitors are Viewing These APA Math Problem Samples:
- Finding the Mean, Median, Mode and the Relative and Cumulative Relative Frequency10 pages/β2750 words | APA | Mathematics & Economics | Math Problem |
- What is the Megatropolis Hospital's Operating Margin?6 pages/β1650 words | No Sources | APA | Mathematics & Economics | Math Problem |
- Solving Systems of Equations1 page/β275 words | No Sources | APA | Mathematics & Economics | Math Problem |
- Research and Describe The Total Cost of Ownership (TOC)1 page/β275 words | 1 Source | APA | Mathematics & Economics | Math Problem |
- Comm 293v Final Mathematics & Economics Math Problem6 pages/β1650 words | No Sources | APA | Mathematics & Economics | Math Problem |
- Economics: The Wealth of Nations by Adam Smith, use of Knowledge in the society by Hayek. Re. . .15 pages/β4125 words | No Sources | APA | Mathematics & Economics | Math Problem |
- Operations Math Problem: Quality Wireless4 pages/β1100 words | No Sources | APA | Mathematics & Economics | Math Problem |