Homotopic refers to a relationship between two continuous functions where one can be transformed into the other through a continuous deformation, such as stretching or bending, without tearing or gluing. This concept is crucial in understanding the fundamental group and its properties because it helps establish when two paths in a topological space can be considered equivalent based on their ability to be continuously deformed into one another. Essentially, homotopy captures the idea of shape and structure in a way that allows mathematicians to classify spaces and paths.
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