ACIT4330 Lecture Notes
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Definitions
Functions
Characteristic Function
Direct Product
Inverse Function
Metric
Power Set
Measure Theory
Sigma-Algebra
Borel Measurable
Borel Sets
Measurable
Measure
Sigma-Algebra
Metric Spaces
Ball
Interior Point
Metric Space
Sets
Complex Numbers
Open Cover
Open Map
Open Sets
Statements
And
Implies
Not
Or
Terminology
Algebraically Complete
Bijective
Bounded
Countable
Injective
QED
Surjective
Topological Spaces
Induced
Initial Topology
Product Topology
Separating Points
Weakest Topology
Terminologies
Compact
Connected
Connected Component
Continuous
Hausdorff
Topological Space
Topology
Tychonoff Theorem
Vector Spaces
Complex Vector Space
Linear Basis
Normed Vector Space
Properties of a Vector Space
Cauchy Sequence
Cauchy-Schwarz Inequality
Hilbert Spaces
Inner Product
Least Upper Bound Property
Linear Map
Nets
Norm
Number Field
Period of a Fraction
Rational Cauchy Sequences
Subcover
Subnet
Excalidraw
Lecture 11
Drawing 2025-02-13 10.57.31.excalidraw
Drawing 2025-02-13 11.02.27.excalidraw
Drawing 2025-02-13 11.26.08.excalidraw
Drawing 2025-02-13 11.47.33.excalidraw
Drawing 2025-02-13 12.01.57.excalidraw
Drawing 2025-02-13 12.07.00.excalidraw
Drawing 2025-02-13 14.01.44.excalidraw
Drawing 2025-02-13 14.06.25.excalidraw
Lecture 12
Drawing 2025-02-24 11.58.37.excalidraw
Drawing 2025-02-24 12.47.32.excalidraw
Lecture 13
Drawing 2025-02-27 13.19.24.excalidraw
Lectures
Lecture 1 - 1.1 Sets and Numbers
Lecture 2
Lecture 3
Lecture 4 - 1.2 Metric Spaces
Lecture 5
Lecture 6 - 2.1 Topology
Lecture 7
Lecture 8
Lecture 11
Lecture 12 - Induced Topologies
Lecture 13 - Measure Theory
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Surjective
Surjective
01 Mar 2025
1 min read
y
∈
Y
∃
x
∈
X
such that
f
(
x
)
=
y
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Bijective
Lecture 3