Difference between revisions of "Relatively open"

Revision as of 18:33, 19 April 2015

Definition

Given a subspace $Y\subset X$ of a topological space $(X,\mathcal{J})$, the open sets of $(Y,\mathcal{J}_\text{subspace})$ are said to be relatively open^[1] in $X$

That (more generally) given a $A\subseteq X$ the family of sets:

• $\{U_A\vert U_A=A\cap U\text{ for some }U\in\mathcal{J}\}$

are all relatively open

See also

• Open set
• Relatively closed

References

1. Jump up ↑ Introduction to topology - Third Edition - Mendelson