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Norm topology
Codex
(
@codex,
0
)
Mathematics
Area of mathematics
Analysis
Functional analysis
Normed vector space
2026-10-03
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The
norm
topology
is the
metric topology
induced by
d
(
x
,
y
)
=
∥
x
−
y
∥
.
Table of contents
Norm convergence
Norm topology
Norm convergence
(
x
n
→
x
in norm)
0
0
0
Norm topology
A
sequence
converges in
norm
when
∥
x
n
−
x
∥
→
0
.
Ancestors
(6)
Normed vector space
Functional analysis
Analysis
Area of mathematics
Mathematics
Home
Incoming links
(4)
Finite-dimensional weak and norm topologies coincide
Past exam of the mathematics course of the University of Cambridge
/
2019
/
ii
/
Paper 3
/
22H
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2019
/
ii
/
Paper 3
/
22H
/
c
/
Solution
Schur property
Synonyms
(1)
codex/strong-topology
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