ThmDex – An index of mathematical definitions, results, and conjectures.
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Deduction system
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Zermelo-Fraenkel set theory
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Set interior
Definition D246
Topologically nowhere dense set
Formulation 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that
(i) $E \subseteq X$
(ii) $\text{cl} E$ is a D88: Set closure for $E$ in $T$
Then $E$ is topologically nowhere dense in $T$ if and only if \begin{equation} \text{int}(\text{cl} E) = \emptyset \end{equation}