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.
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 \( Y \).
New to topics? Read the docs here!