Point-Set Topology Video Tutorials

Video Lectures

Displaying all 29 video lectures.
Lecture 1
Metrics
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Metrics
Introduction to Metrics
Lecture 2
Metric Examples (Part 1)
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Metric Examples (Part 1)
The Euclidean Metric
Lecture 3
Metric Examples (Part 2)
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Metric Examples (Part 2)
The Discrete Metric, the Max Metric and the Taxicab Metric.
Lecture 4
Open Balls
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Open Balls
Open Balls in a Metric Space
Lecture 5
Open Sets
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Open Sets
Open Sets in a Metric Space
Lecture 6
Continuity of Functions Between Metric Spaces (Part 1)
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Continuity of Functions Between Metric Spaces (Part 1)
Continuity of Functions Between Metric Spaces
Lecture 7
Continuity of Functions Between Metric Spaces (Part 2)
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Continuity of Functions Between Metric Spaces (Part 2)
Alternate definition of continuity between metric spaces.
Lecture 8
Unions and Intersections of Open Sets In Metric Spaces
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Unions and Intersections of Open Sets In Metric Spaces
Unions and Intersections of Open Sets in Metric Spaces
Lecture 9
Topological Spaces
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Topological Spaces
Definition of a Topology and a Topological Space
Lecture 10
Topology Examples
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Topology Examples
Examples of Topological Spaces
Lecture 11
Metric Equivalences
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Metric Equivalences
Equivalence of two Metric Topologies
Lecture 12
Continuity of Functions Between Topological Spaces
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Continuity of Functions Between Topological Spaces
Continuity of functions between Topological Spaces, continuity of constant functions, composition of continuous functions
Lecture 13
Continuity Examples
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Continuity Examples
Examples of continuous and discontinuous functions between topological spaces
Lecture 14
Closed Sets
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Closed Sets
Closed sets in a topological space
Lecture 15
Properties of Closed Sets
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Properties of Closed Sets
Properties of closed sets in a topological space.
Lecture 16
Bases
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Bases
Bases for a Topology
Lecture 17
Subbases
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Subbases
Subbases for a topology
Lecture 18
Topological Distinguishability
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Topological Distinguishability
Courseness and fineness, topological distinguishability of points.
Lecture 19
Neighbourhoods and Interiors
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Neighbourhoods and Interiors
Neighbourhoods of points and interiors of sets.
Lecture 20
Neighbourhood Bases
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Neighbourhood Bases
Neighbourhood Bases in a topological space
Lecture 21
Axioms Of Countability
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Axioms Of Countability
First countable and second countable topological spaces
Lecture 22
Sequences (Part 1)
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Sequences (Part 1)
Definition of sequences in a topological space
Lecture 23
Sequences (Part 2)
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Sequences (Part 2)
Subsequences, Cluster Points, Examples of sequences in topological spaces
Lecture 24
Sequential Continuity
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Sequential Continuity
Sequentially continuous functions between topological spaces
Lecture 25
Sequential Continuity Counterexample
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Sequential Continuity Counterexample
A sequentially continuous noncontinuous function with a non first countable domain
Lecture 26
Directed Sets
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Directed Sets
Introduction to directed sets.
Lecture 27
Nets
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Nets
Introduction to nets in topological spaces
Lecture 28
Subnets
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Subnets
Subnets and cluster points of nets
Lecture 29
Net Continuity
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Net Continuity
Continuity in terms of nets