Category:Everywhere Dense
Jump to navigation
Jump to search
This category contains results about Everywhere Dense.
Definitions specific to this category can be found in Definitions/Everywhere Dense.
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$ be a subset.
Definition 1
The subset $H$ is (everywhere) dense in $T$ if and only if:
- $H^- = S$
where $H^-$ is the closure of $H$.
Definition 2
The subset $H$ is (everywhere) dense in $T$ if and only if the intersection of $H$ with every non-empty open set of $T$ is non-empty:
- $\forall U \in \tau \setminus \set \O: H \cap U \ne \O$
Definition 3
The subset $H$ is (everywhere) dense in $T$ if and only if every neighborhood of every point of $S$ contains at least one point of $H$.
Pages in category "Everywhere Dense"
This category contains only the following page.