Open mindset fallacy

From Oxford Languages:

• close-mind·ed, adjective: having or showing rigid opinions or a narrow outlook
• o·pen-mind·ed, adjective: willing to consider new ideas; unprejudiced.

"Willing to consider new ideas" is an idea. Subscribing to a single idea is rigid & a narrow outlook, as you are not considering the negation of that idea: not willing to consider new ideas.

Being strictly open-minded is close-minded by definition. Languages in theory of computation and metric spaces in real analysis are topics that give some intuition to this set theoretic way of thinking.