If $(X, \tau_X)$ is a topological space, then the weight is usually defined as follows: $$w(X) = \min \{ \vert B \vert : B \subset \wp(X), B \mathrm{\; is \; a \; basis \; of \;} \tau_X \}$$ I was wondering why this is a minimum and not an infimum. Does anyone know an argument for this?
Thanks for every answer!