1 normed and banach spaces

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Concepts

File	status	type	Lectures
Baire Category Theorem	complete	🧮	Functional Analysis Lecture 4 Functional Analysis Lecture 3
Banach space	complete	💡	Functional Analysis Lecture 2 Lecture 23 Functional Analysis Lecture 6 Functional Analysis Lecture 11 Functional Analysis Lecture 13 Functional Analysis Lecture 4 Functional Analysis Lecture 3 Functional Analysis Lecture 1
banach spaces have all absolutely summable series are summable	complete	🧮	Functional Analysis Lecture 2 Functional Analysis Lecture 13
bijective bounded linear operators have bounded linear inverses	complete	🧮	Functional Analysis Lecture 4
bounded linear operator space is banach	complete	💡	Functional Analysis Lecture 2 Functional Analysis Lecture 3
chain	complete	💡	Functional Analysis Lecture 4 Functional Analysis Lecture 5
closed graph theorem	complete	🧮	Functional Analysis Lecture 4
closed subspaces of banach spaces are banach	complete	🧮	Functional Analysis Lecture 3
complete metric spaces have banach continuous bounded function spaces	complete	🧮	Functional Analysis Lecture 2 Functional Analysis Lecture 1
continuity for linear functions	complete	🧮	Functional Analysis Lecture 2 Lecture 37 Lecture 36 Lecture 25 Lecture 26 Lecture 24 2025-03-05 graphs lecture 12 Functional Analysis Lecture 6 Functional Analysis Lecture 15 Functional Analysis Lecture 4 Functional Analysis Lecture 17 Functional Analysis Lecture 5 Functional Analysis Lecture 19
continuous bounded function space	complete	💡	Functional Analysis Lecture 1
continuous linear function space	complete	💡	Functional Analysis Lecture 2 Lecture 25 Functional Analysis Lecture 3 Functional Analysis Lecture 19
continuous map	complete	💡	Functional Analysis Lecture 2 Functional Analysis Lecture 8 Functional Analysis Lecture 15 Functional Analysis Lecture 9 Functional Analysis Lecture 13 Functional Analysis Lecture 4 Functional Analysis Lecture 3 Functional Analysis Lecture 17 Functional Analysis Lecture 5
corollary of Hahn-Banach	complete	🧮	Functional Analysis Lecture 6
double dual	complete	💡	Functional Analysis Lecture 6
every vector space has a hamel basis	complete	🧮	Functional Analysis Lecture 5
finite vector space	complete	💡	Functional Analysis Lecture 19 Functional Analysis Lecture 1
Hahn-Banach theorem	complete	🧮	Lecture 27 Functional Analysis Lecture 6 Functional Analysis Lecture 4 Functional Analysis Lecture 5
Hamel basis	complete	💡	Functional Analysis Lecture 4 Functional Analysis Lecture 5
infinity norm for continuous bounded function space	complete	💡	Functional Analysis Lecture 1
isometric	complete	💡	Random Matrix Lecture 02 Random Matrix Lecture 05 Functional Analysis Lecture 6 Functional Analysis Lecture 15
l-p vector space	complete	💡	Functional Analysis Lecture 15 Functional Analysis Lecture 13 Functional Analysis Lecture 1
linear function	complete	💡	Functional Analysis Lecture 2 Lecture 25 Lecture 24 Lecture 01 Random Matrix Lecture 02 Random Matrix Lecture 01 2025-03-31 lecture 16 Functional Analysis Lecture 6 Functional Analysis Lecture 15 Functional Analysis Lecture 4 Functional Analysis Lecture 17 Functional Analysis Lecture 5
maximal element	complete	💡	Functional Analysis Lecture 4 Functional Analysis Lecture 5
open mapping theorem	complete	🧮	Functional Analysis Lecture 4
operator norm	complete	💡	Functional Analysis Lecture 2 Lecture 36 Lecture 25 Lecture 26 Lecture 27 2025-04-02 lecture 17 2025-03-05 graphs lecture 12 Random Matrix Lecture 04 2025-04-14 lecture 20 2025-03-26 lecture 15 Functional Analysis Lecture 3 Functional Analysis Lecture 17
partial order	complete	💡	Functional Analysis Lecture 4 Functional Analysis Lecture 5
quotient of a vector space	complete	💡	Functional Analysis Lecture 3
reflexive banach space	complete	💡	Functional Analysis Lecture 6
semi-norm	complete	💡	Random Matrix Lecture 04 Functional Analysis Lecture 6 Functional Analysis Lecture 13 Functional Analysis Lecture 3 Functional Analysis Lecture 1
subspace	complete	💡	Lecture 02 Random Matrix Lecture 06 Random Matrix Lecture 07 Functional Analysis Lecture 3 Functional Analysis Lecture 17 Functional Analysis Lecture 5 Functional Analysis Lecture 19
summable series	complete	💡	Functional Analysis Lecture 2 Functional Analysis Lecture 13 Functional Analysis Lecture 4
the cartesian product of banach spaces is banach	complete	🧮	Functional Analysis Lecture 4
the functional to the double dual is isometric	complete	🧮	Functional Analysis Lecture 6
uniform boundedness theorem	complete	🧮	Functional Analysis Lecture 3
upper bound	complete	💡	Functional Analysis Lecture 4 Functional Analysis Lecture 5
we can always extend functions on subspaces	in progress	🧮	Functional Analysis Lecture 5
Zorn's lemma	complete	🧮	Functional Analysis Lecture 4 Functional Analysis Lecture 5

Mentions

File
Baire Category Theorem
Banach space
Hahn-Banach theorem
Hamel basis
Zorn's lemma
banach spaces have all absolutely summable series are summable
bijective bounded linear operators have bounded linear inverses
bounded linear operator space is banach
chain
closed graph theorem
closed subspaces of banach spaces are banach
complete metric spaces have banach continuous bounded function spaces
continuity for linear functions
continuous bounded function space
continuous linear function space
continuous map
corollary of Hahn-Banach
double dual
every vector space has a hamel basis
finite vector space
infinity norm for continuous bounded function space
isometric
l-p vector space
linear function
maximal element
open mapping theorem
operator norm
partial order
quotient of a vector space
reflexive banach space
semi-norm
subspace
summable series
the cartesian product of banach spaces is banach
the functional to the double dual is isometric
uniform boundedness theorem
upper bound
we can always extend functions on subspaces

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