# Point-Set Topology Video Tutorials

## Video Lectures

Displaying all 29 video lectures.

Lecture 1Play Video |
MetricsIntroduction to Metrics |

Lecture 2Play Video |
Metric Examples (Part 1)The Euclidean Metric |

Lecture 3Play Video |
Metric Examples (Part 2)The Discrete Metric, the Max Metric and the Taxicab Metric. |

Lecture 4Play Video |
Open BallsOpen Balls in a Metric Space |

Lecture 5Play Video |
Open SetsOpen Sets in a Metric Space |

Lecture 6Play Video |
Continuity of Functions Between Metric Spaces (Part 1)Continuity of Functions Between Metric Spaces |

Lecture 7Play Video |
Continuity of Functions Between Metric Spaces (Part 2)Alternate definition of continuity between metric spaces. |

Lecture 8Play Video |
Unions and Intersections of Open Sets In Metric SpacesUnions and Intersections of Open Sets in Metric Spaces |

Lecture 9Play Video |
Topological SpacesDefinition of a Topology and a Topological Space |

Lecture 10Play Video |
Topology ExamplesExamples of Topological Spaces |

Lecture 11Play Video |
Metric EquivalencesEquivalence of two Metric Topologies |

Lecture 12Play Video |
Continuity of Functions Between Topological SpacesContinuity of functions between Topological Spaces, continuity of constant functions, composition of continuous functions |

Lecture 13Play Video |
Continuity ExamplesExamples of continuous and discontinuous functions between topological spaces |

Lecture 14Play Video |
Closed SetsClosed sets in a topological space |

Lecture 15Play Video |
Properties of Closed SetsProperties of closed sets in a topological space. |

Lecture 16Play Video |
BasesBases for a Topology |

Lecture 17Play Video |
SubbasesSubbases for a topology |

Lecture 18Play Video |
Topological DistinguishabilityCourseness and fineness, topological distinguishability of points. |

Lecture 19Play Video |
Neighbourhoods and InteriorsNeighbourhoods of points and interiors of sets. |

Lecture 20Play Video |
Neighbourhood BasesNeighbourhood Bases in a topological space |

Lecture 21Play Video |
Axioms Of CountabilityFirst countable and second countable topological spaces |

Lecture 22Play Video |
Sequences (Part 1)Definition of sequences in a topological space |

Lecture 23Play Video |
Sequences (Part 2)Subsequences, Cluster Points, Examples of sequences in topological spaces |

Lecture 24Play Video |
Sequential ContinuitySequentially continuous functions between topological spaces |

Lecture 25Play Video |
Sequential Continuity CounterexampleA sequentially continuous noncontinuous function with a non first countable domain |

Lecture 26Play Video |
Directed SetsIntroduction to directed sets. |

Lecture 27Play Video |
NetsIntroduction to nets in topological spaces |

Lecture 28Play Video |
SubnetsSubnets and cluster points of nets |

Lecture 29Play Video |
Net ContinuityContinuity in terms of nets |