Homotopy equivalence is a concept in topology that indicates two spaces can be transformed into each other through continuous deformations, implying they share the same topological properties. This relationship is established when there exist continuous maps between the two spaces that can be 'reversed' through homotopies, making them fundamentally the same from a topological perspective. The idea connects closely with various fundamental concepts in algebraic topology, influencing how we understand the structure and classification of spaces.
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