Definition:Dense-in-itself
This page is about Dense-in-itself in the context of topology. For other uses, see Dense.
Definition
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$.
Then $H$ is dense-in-itself if and only if it contains no isolated points.
Also see
- Results about topological denseness can be found here.
Sources
- 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Limit Points
As such, the following source works, along with any process flow, will need to be reviewed.
Specifically: Analyse and present the result that rational numbers are dense in reals
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- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: dense set
