Difference between revisions of "Relatively open"
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Given a [[Subspace topology|subspace]] {{M|Y\subset X}} of a [[Topological space|topological space]] {{M|(X,\mathcal{J})}}, the open sets of {{M|(Y,\mathcal{J}_\text{subspace})}} are said to be '''relatively open'''<ref>Introduction to topology - Third Edition - Mendelson</ref> in {{M|X}} | Given a [[Subspace topology|subspace]] {{M|Y\subset X}} of a [[Topological space|topological space]] {{M|(X,\mathcal{J})}}, the open sets of {{M|(Y,\mathcal{J}_\text{subspace})}} are said to be '''relatively open'''<ref>Introduction to topology - Third Edition - Mendelson</ref> in {{M|X}} | ||
| − | + | Alternatively we may say given a {{M|A\subseteq X}} the family of sets: | |
* {{M|1=\{U_A\vert U_A=A\cap U\text{ for some }U\in\mathcal{J}\} }} | * {{M|1=\{U_A\vert U_A=A\cap U\text{ for some }U\in\mathcal{J}\} }} | ||
| − | are all relatively open | + | are all ''relatively open in {{M|A}}'' |
==See also== | ==See also== | ||
Latest revision as of 18:42, 19 April 2015
Definition
Given a subspace Y⊂X of a topological space (X,J), the open sets of (Y,Jsubspace) are said to be relatively open[1] in X
Alternatively we may say given a A⊆X the family of sets:
- {UA|UA=A∩U for some U∈J}
are all relatively open in A
See also
References
- Jump up ↑ Introduction to topology - Third Edition - Mendelson
