Algebraic Topology

Isotopy, Ambient Isotopy, Homotopy, Retracts, and Deformation Retracts

Isotopic Embeddings on Topological Spaces
Isotopic and Non-Isotopic Embeddings on the Bounded Cone
Ambient Isotopic Embeddings on Topological Spaces
Homotopic Mappings Relative to a Subset of a Topological Space
Homotopically Equivalent Topological Spaces
Homeomorphic Topological Spaces are Homotopically Equivalent
Retract Subspaces of a Topological Space
Deformation Retract Subspaces of a Topological Space

Fundamental Groups of a Topological Space

Products of Paths Relative to {0, 1} in a Topological Space
Associativity of Products of Paths in a Topological Space
Constant Paths in a Topological Space
Inverse Paths in a Topological Spaces
The Fundamental Group of a Topological Space at a Point
Fundamental Groups under Homeomorphisms on Topological Spaces
Simply Connected Topological Spaces
The Fundamental Groups of a Path Connected Topological Space are Isomorphic
The Fundamental Groups of Discrete and Indiscrete Topological Spaces
The Induced Mapping from the Fundamental Groups of Two Topological Spaces
The Fundamental Group of a Topological Product
The Fundamental Group of the Cylinder and the Torus
An Example of a Retract that is NOT a Deformation Retract

Brouwer's Fixed Point Theorem

Brouwer's Fixed Point Theorem
Solutions to Systems of Equations by Brouwer's Fixed Point Theorem
The Jordan Curve Theorem

Group Presentations

Words Over a Set
Group Presentations
A Group Presentation for Zn
A Group Presentation for S3
Tietze Transformations
Tietze Transformations Example 1
Tietze Transformations Example 2
The Free Product of Groups

The Seifert-van Kampen Theorem

The Seifert-van Kampen Theorem
The Seifert-van Kampen Theorem Example 1
The Seifert-van Kampen Theorem Example 2
The Seifert-van Kampen Theorem Example 3

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