1 normed and banach spaces

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Concepts

File	status	type	Lectures
Baire Category Theorem	complete	🧮	Functional Analysis Lecture 3 Functional Analysis Lecture 4
Banach space	complete	💡	Functional Analysis Lecture 2 Lecture 23 Functional Analysis Lecture 1 Functional Analysis Lecture 3 Functional Analysis Lecture 4
banach spaces have all absolutely summable series are summable	complete	🧮	Functional Analysis Lecture 2
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
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 2025-03-05 graphs lecture 12 Lecture 24 Lecture 25 Lecture 26 Lecture 36 Lecture 37 Functional Analysis Lecture 4
continuous bounded function space	complete	💡	Functional Analysis Lecture 1
continuous linear function space	complete	💡	Functional Analysis Lecture 2 Lecture 25 Functional Analysis Lecture 3
continuous map	complete	💡	Functional Analysis Lecture 2 Functional Analysis Lecture 3 Functional Analysis Lecture 4
finite vector space	complete	💡	Functional Analysis Lecture 1
Hamel basis	complete	💡	Functional Analysis Lecture 4
infinity norm for continuous bounded function space	complete	💡	Functional Analysis Lecture 1
l-p vector space	complete	💡	Functional Analysis Lecture 1
linear function	complete	💡	Functional Analysis Lecture 2 2025-03-31 lecture 16 Lecture 01 Lecture 24 Lecture 25 Functional Analysis Lecture 4
maximal element	complete	💡	Functional Analysis Lecture 4
open mapping theorem	complete	🧮	Functional Analysis Lecture 4
operator norm	complete	💡	Functional Analysis Lecture 2 2025-04-02 lecture 17 2025-03-05 graphs lecture 12 2025-03-26 lecture 15 2025-04-14 lecture 20 Lecture 25 Lecture 26 Lecture 27 Lecture 36 Functional Analysis Lecture 3
partial order	complete	💡	Functional Analysis Lecture 4
quotient of a vector space	complete	💡	Functional Analysis Lecture 3
semi-norm	complete	💡	Functional Analysis Lecture 1 Functional Analysis Lecture 3
subspace	complete	💡	Lecture 02 Functional Analysis Lecture 3
summable series	complete	💡	Functional Analysis Lecture 2 Functional Analysis Lecture 4
the cartesian product of banach spaces is banach	complete	🧮	Functional Analysis Lecture 4
uniform boundedness theorem	complete	🧮	Functional Analysis Lecture 3
upper bound	complete	💡	Functional Analysis Lecture 4
Zorn's lemma	complete	🧮	Functional Analysis Lecture 4

Mentions

File
Baire Category Theorem
Banach space
banach spaces have all absolutely summable series are summable
bijective bounded linear operators have bounded linear inverses
bounded linear operator space is banach
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
finite vector space
infinity norm for continuous bounded function space
l-p vector space
linear function
open mapping theorem
operator norm
quotient of a vector space
semi-norm
subspace
summable series
the cartesian product of banach spaces is banach
uniform boundedness theorem
closed graph theorem
partial order
upper bound
maximal element
chain
Hamel basis
Zorn's lemma

Created 2025-05-29 Last Modified 2025-05-29