About half of the ones that I understand what they mean seem perfectly plausible to me. We need a page that explains why they are false. For example can someon

About half of the ones that I understand what they mean seem perfectly plausible to me. We need a page that explains why they are false. For example can someone explain "Every connected component of a topological space is open and closed." Edit: found it on wikipedia: "The components in general need not be open: the components of the rational numbers, for instance, are the one-point sets."