Proof of C[a,b] is not Compact | L7 | Compactness @ranjankhatu

Показать описание

Proof of C[a,b] is not Compact | L7 | Compactness @Ranjan Khatu
#ranjankhatu
#notCompact
#C[a,b]
#example

Check the following Playlists on the Topics
1. Line Integrals
2. Calculus- Unit 1
3. Complex Analysis
4. Series
5. Triple Integration

6. Metric Spaces
7. Double Integration

8. Applications of Laplace Transforms
9. Laplace Transforms

10. Indefinite and Improper Integrals

11. Riemann Integration
12. Limits and Continuity
13. Basic Complex Analysis

14. Continuous Functions
15. Function

16. Beta and Gamma Functions
17. IIT JAM | Double and Triple Integration
18. Surface Integrals
19. Compact Metric Space

Ranjan Khatu

Рекомендации по теме

Комментарии

Sir, if f, g belongs to C[a, b] then in this example what will be d(f, g) ?
Actually I didn't get the rule of the metric. f is a member in C[a, b], didn't we req another function to measure the distance between them ? Now |f(x)| can be expressed as |f(x)-0| i.e. we can take g(x)=0. But isn't it a specific case ? How it is a metric if we can't measure distance (metric distance) between two functions ? It will be a case if we take sup{|f(x)-g(x)| : a<x<b}. But how the given question can be correct ?

pritambasu

Proof of C[a,b] is not Compact | L7 | Compactness @ranjankhatu

Proof: Divides Relation is Transitive (if a divides b and b divides c then a divides c)

Direct Proof: If a|b and b|c, then a|c

Number Theory Proof: If a|b and b|a then a = b or a = -b

Digital Electronics: Proof of a Boolean Identity (A+A'B=A+B)

Divisibility Proof with the Sorcerer: a|b and a|c implies a|(b + c)

Set Theory Proof: Prove that the Relative Complement Distributes over the Intersection of Sets

Proof that if g o f is Surjective(Onto) then g is Surjective(Onto)

Proof: If det(A) != 0 and AB = AC, then B = C

Intro to Linear Algebra - A few words on the proof of the Invertible Matrix Theorem (Sec 2.3, B)

Proof by Contradiction: There are no integers x and y such that x^2 = 4y + 2

Pythagorean theorem proof by scaling

Set Theory Proof: A x C is a Subset of B x C if and only if A is a Subset of B

Proof: If A is a Subset of B then C-B is a Subset of C-A | Set Theory

Set Theory Proof: If A n B = empty! then A is a subset of B complement

Proof by Contradiction | Method & First Example

Proof: A is a Subset of B iff A Union B Equals B | Set Theory, Subsets

Set Theory Proof A is a subset of B if and only if A intersect B = A

Proof of A △ (B △ C) = (A △ B) △ C (Associativity of the Symmetric Difference)

Proof with Sets Example with Intersection and Union

Proof for c= E/B relationships between velocity of the light magnetic field and electric field

Conditional Statements: if p then q

Demorgan's Law Proof

Proof that if g o f is Injective(one-to-one) then f is Injective(one-to-one)

An Example Proof using Identities of Regular Expressions