ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Subset structure
Topological space
Isolated point
Set of isolated points
Definition D247
Topologically self-dense set
Formulation 0
Let $T = (X, \mathcal{T})$ be a D1106: Topological space such that
(i) $E \subseteq X$ is a D78: Subset
(ii) $\mathcal{I} : = \mathcal{I}_T(E)$ is the D3876: Set of isolated points of $E$ in $T$
Then $E$ is a topologically self-dense in $T$ if and only if \begin{equation} \mathcal{I} = \emptyset \end{equation}