Notice how we never remove deleted keys from the map. This is one drawback to CRDTs — we can only ever add information, not remove it. Although from the application’s perspective the key has been fully deleted, the underlying state still records that the key was once there. In technical terms, we say that CRDTs are monotonically increasing data structures.9
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\(f^{-1}\) is continuous (images of open sets are open, i.e. \(f\) is an open map).