Understanding Topology in Algebra
Topology studies the properties of space that are preserved under continuous transformations. It is a branch of mathematics closely related to geometry and analysis.
What is Topology?
Topology focuses on properties like continuity, connectedness, and compactness.
Open and Closed Sets
An open set does not include its boundary points; a closed set does.
Homeomorphism
A homeomorphism is a continuous deformation between two shapes, showing they are topologically equivalent.
Practice Problems
- Is a circle homeomorphic to a square?
- Give an example of an open set in \( \mathbb{R}^2 \).
- What is a topological space?
📋
↑