If $A\subset B$ and $B$ is a metric space. What is the difference between "$A$ open subset of $B$" and "$A$ open relative to $B$"?
Difference between 'A open subset of B' and 'A open relative to B'
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general-topology
metric-spaces
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6A open relative to B is often used to express the fact that A is open in the subspace topology http://en.wikipedia.org/wiki/Subspace_topology This would howerver require a slightly different setting than you described - you would need a larger space which contains B. – 2011-07-17