In mathematics, particularly in category theory and algebraic topology, the smash product is a specific operation that combines two pointed spaces or pointed sets. The smash product is denoted by \( X \wedge Y \), where \( X \) and \( Y \) are pointed spaces, meaning that each has a distinguished 'base point.
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For based spaces, the smash product iswhere the wedge consists of pairs having at least one basepoint coordinate.