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Videos about topology.

Indexed Families of Sets

Indexed Families of Sets

Functions (Domain, Codomain, Range, Image, and Graph)

Functions (Domain, Codomain, Range, Image, and Graph)

Functions (Well-defined, Injective, Surjective, Bijective)

Functions (Well-defined, Injective, Surjective, Bijective)

Functions (inverses and preimages/inverse images)

Functions (inverses and preimages/inverse images)

Functions (Commutative Diagrams)

Functions (Commutative Diagrams)

Metrics (definition and examples)

Metrics (definition and examples)

Proof that the Discrete Metric is a metric

Proof that the Discrete Metric is a metric

The Taxicab Metric on R^n

The Taxicab Metric on R^n

Open Balls in a Metric Space

Open Balls in a Metric Space

Continuity in a metric space

Continuity in a metric space

Open sets in a metric space

Open sets in a metric space

Example of continuous function between two metric spaces

Example of continuous function between two metric spaces

Product metrics (revised)

Product metrics (revised)

Cauchy sequences in metric spaces

Cauchy sequences in metric spaces

Complete metric spaces

Complete metric spaces

Epsilon nets and totally bounded metric spaces

Epsilon nets and totally bounded metric spaces

Open covers and compact metric spaces

Open covers and compact metric spaces

Finite intersection property and compactness

Finite intersection property and compactness

Topology on a set

Topology on a set

The Discrete Metric Generates the Discrete Topology

The Discrete Metric Generates the Discrete Topology

Topological spaces

Topological spaces

More topological spaces, finer and courser

More topological spaces, finer and courser

Basis for topology (intro)

Basis for topology (intro)

Characterization for a basis of a topology

Characterization for a basis of a topology

Equivalent bases for a topology

Equivalent bases for a topology

Basis for the Lower Limit Topology?

Basis for the Lower Limit Topology?

Basis for the Usual Topology on R?

Basis for the Usual Topology on R?

Subbasis for a topology

Subbasis for a topology

Subbasis for Some Topology on R^2 that is NOT a Basis or ANY Topology on R^2

Subbasis for Some Topology on R^2 that is NOT a Basis or ANY Topology on R^2

Local Basis at a Point and First Countable Spaces

Local Basis at a Point and First Countable Spaces

Second Countable Spaces, and the relation to First Countable Spaces

Second Countable Spaces, and the relation to First Countable Spaces

Closed sets

Closure of a Set

Closure of a Set

Unions and Intersections of Closures

Unions and Intersections of Closures

Boundary of a set

Boundary of a set

Dense subset

Interior of a set

Interior of a set

Unions and Intersections of Interiors

Unions and Intersections of Interiors

Convergent sequences in topological spaces

Convergent sequences in topological spaces

Hausdorff spaces

Hausdorff spaces

Every Singleton in a Hausdorff Space is Closed

Every Singleton in a Hausdorff Space is Closed

Continuity (topological sense, definition)

Continuity (topological sense, definition)

Continuity (topological sense, characterization,), open and closed maps

Continuity (topological sense, characterization,), open and closed maps

Product topology for two spaces

Product topology for two spaces

Product topology on big products

Product topology on big products

Quotient topology

Quotient topology

Quotient Topology for Equivalence Relations (Identification Spaces)

Quotient Topology for Equivalence Relations (Identification Spaces)

Intro to connected spaces

Intro to connected spaces

Facts about connected spaces

Facts about connected spaces

Pathwise connected topological space

Pathwise connected topological space

T_0 spaces: definition and examples

T_0 spaces: definition and examples

T_1 Spaces: definition and relation to T_0 and T_2 (Hausdorff) Spaces

T_1 Spaces: definition and relation to T_0 and T_2 (Hausdorff) Spaces

A Characterization of T_1 Spaces

A Characterization of T_1 Spaces

Open sets and Neighborhoods of a Point

Open sets and Neighborhoods of a Point

Complete System of Neighborhoods of a Point

Complete System of Neighborhoods of a Point

Axioms for a Complete System of Neighborhoods for a Point in a Topological Space

Axioms for a Complete System of Neighborhoods for a Point in a Topological Space

Neighborhood Space (Topology)

Neighborhood Space (Topology)

Product Topology on an Infinite Product of Topological Spaces

Product Topology on an Infinite Product of Topological Spaces

A Problem Concerning the Quotient Topology and Closed, Continuous, Surjective Maps

A Problem Concerning the Quotient Topology and Closed, Continuous, Surjective Maps

An Easy Quotient Topology Problem

An Easy Quotient Topology Problem

Basic Topology of the Complex Plane

Basic Topology of the Complex Plane

Distance from a point to a set is Lipschitz

Distance from a point to a set is Lipschitz

The Finite Complement Topology

The Finite Complement Topology

Quick Intro to Homeomorphisms

Quick Intro to Homeomorphisms

Homeomorphism and The Hausdorff Property

Homeomorphism and The Hausdorff Property

Homeomorphism and Connectedness

Homeomorphism and Connectedness

Euclidean Space, Locally Euclidean Space, and Manifolds

Euclidean Space, Locally Euclidean Space, and Manifolds

The Axiom of Choice: History, Intuition, and Conflict

The Axiom of Choice: History, Intuition, and Conflict

Piecewise Continuous Linear Functions are Dense Among Continuous Functions

Piecewise Continuous Linear Functions are Dense Among Continuous Functions

Understand The Baire Category Theorem: Dense Sets, Nowhere Dense Sets, & Infinity

Understand The Baire Category Theorem: Dense Sets, Nowhere Dense Sets, & Infinity

The Alexander Subbase Theorem: help understanding the definitions and the proof

The Alexander Subbase Theorem: help understanding the definitions and the proof

Paths and the Path Product

Paths and the Path Product

Homotopy Intro

Homotopy Classes, the Path Product, and Associativity

Homotopy Classes, the Path Product, and Associativity