Topology

Study of geometric properties preserved under continuous deformations.

What is Topology?Types of Topological SpacesOpen and Closed Sets
Homeomorphisms and Topological EquivalenceConnectedness and CompactnessTopological Invariants
Topology in Computer ScienceTopology in Biology and MedicineEveryday Uses of Topology
Visual Learning with DiagramsActive Recall and Practice Problems
What is Topology?Types of Topological...Open and Closed SetsHomeomorphisms and T...Connectedness and Co...Topological Invarian...Topology in Computer...Topology in Biology ...Everyday Uses of Top...Visual Learning with...Active Recall and Pr...
Practical Applications

Topology in Computer Science

How Computers Use Topology

Topology plays a big role in computer science, especially in data analysis, graphics, and networking.

Key Applications

  • Data analysis: Topological Data Analysis (TDA) helps find patterns in complex data by studying the “shape” of data clouds.
  • Computer graphics: Topology helps create and manipulate 3D models for games and movies.
  • Network theory: Topological ideas help design efficient and robust communication networks.

Fun Uses

  • Analyzing the spread of information in social networks.
  • Mapping the surface of a video game character to animate it realistically.

Examples

  • Using TDA to discover shapes in high-dimensional data for cancer research.

  • Designing realistic animated characters using topological meshes in 3D software.

Next
Topology in Biology and Medicine