\(f^{-1}\) is continuous (images of open sets are open, i.e. \(f\) is an open map).
A guilty pleasure is something you genuinely like, but that clashes with your self image. For example, you might really be a fan of Paris Hilton, but feel that you’re the kind of person who should not be a fan of Paris Hilton. If you ever tell someone you like Paris Hilton, you’ll say it with just enough coyness that your interlocutor will understand that you shouldn’t be mistaken for that kind of person.
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一息もつけない…子どもの付き添い入院 国の支援も進まず なぜ