A topological invariant is a property of a topological space that remains unchanged under continuous deformations, such as stretching or bending, but not tearing or gluing. This concept is important in understanding the geometric properties of shapes and spaces, as it helps classify them based on their intrinsic qualities rather than their specific forms. Topological invariants play a crucial role in the analysis of surfaces and manifolds, especially when exploring relationships between curvature and topology.
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