Difference between revisions of "Relatively open"
From Maths
(Created page with "==Definition== Given a subspace {{M|Y\subset X}} of a topological space {{M|(X,\mathcal{J})}}, the open sets of {{M|(Y,\mathcal{J}_...") |
m |
||
| Line 8: | Line 8: | ||
==See also== | ==See also== | ||
* [[Open set]] | * [[Open set]] | ||
| + | * [[Relatively closed]] | ||
==References== | ==References== | ||
Revision as of 18:33, 19 April 2015
Definition
Given a subspace [ilmath]Y\subset X[/ilmath] of a topological space [ilmath](X,\mathcal{J})[/ilmath], the open sets of [ilmath](Y,\mathcal{J}_\text{subspace})[/ilmath] are said to be relatively open[1] in [ilmath]X[/ilmath]
That (more generally) given a [ilmath]A\subseteq X[/ilmath] the family of sets:
- [ilmath]\{U_A\vert U_A=A\cap U\text{ for some }U\in\mathcal{J}\}[/ilmath]
are all relatively open
See also
References
- ↑ Introduction to topology - Third Edition - Mendelson
