Relatively open

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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]

Alternatively we may say 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 in [ilmath]A[/ilmath]

See also

References

  1. Introduction to topology - Third Edition - Mendelson