Define topology
Understand the Problem
The question is asking for the definition of topology, a branch of mathematics that deals with the properties of space that are preserved under continuous transformations. This can involve concepts such as open and closed sets, continuity, and compactness, among others.
Answer
Topology studies properties of geometric objects preserved under continuous deformations.
Topology is the branch of mathematics that studies properties of geometric objects that are preserved under continuous deformations, such as stretching or bending, without tearing or gluing. It is sometimes referred to as 'rubber-sheet geometry'.
Answer for screen readers
Topology is the branch of mathematics that studies properties of geometric objects that are preserved under continuous deformations, such as stretching or bending, without tearing or gluing. It is sometimes referred to as 'rubber-sheet geometry'.
More Information
Topology is foundational to many areas of mathematics, including analysis and geometry. It helps describe various physical and abstract spaces crucial in both theoretical and applied sciences.
Sources
- Topology - Wikipedia - en.wikipedia.org
- What is Topology? | Pure Mathematics - University of Waterloo - uwaterloo.ca
- Topology | Types, Properties & Examples | Britannica - britannica.com
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