I was recently reading Chapter 3 on meromorphic functions in "Complex Analysis by Stein and Shakarchi". They mentioned that the property that holomorphic functions are open mappings is a geometric property. My question is that why openness is a geometric property? I know openness, closeness, compactness, and connectedness are concepts in topology, but I still can't understand intuitively why the openness and closeness of a map is geometric property.
2026-03-28 10:03:20.1774692200
Why is open mapping a geometric property?
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