An open map sends each open set to an open set; a closed map sends each closed set to a closed set. These properties concern images, whereas continuity concerns inverse images of open sets. Neither openness nor closedness alone implies continuity.
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In topology, "open" and "closed" maps are concepts that describe certain properties of functions between topological spaces. Here's a brief explanation of each term: ### Open Maps A function \( f: X \rightarrow Y \) between two topological spaces is called an **open map** if it takes open sets in \( X \) to open sets in \( Y \).