If such an \(f\) exists, \(X\) and \(Y\) are called homeomorphic, written \(X \cong Y\).
Meta was recently granted a patent in Dec, 2025 that would essentially allow the social media platform to post on a dormant user’s behalf—whether they took a break from social media or long after they’ve passed away. The patent, first filed in 2023, describes a large language model that “simulates” a user’s social media activity, using a user’s comments, likes, or content to respond to other users and also references technology that would simulate video or audio calls with users.
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