Homotopy equivalent refers to a relationship between two topological spaces that can be continuously deformed into each other through a series of transformations called homotopies. This concept shows that even if two spaces look different, they can have the same topological properties, making them fundamentally similar. The significance of homotopy equivalence lies in its ability to preserve important features such as connectedness and the number of holes, which are crucial for understanding the structure of spaces in algebraic topology.
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