In my book for projective geometry, this symbol: < x > means a subspace containing points x. But my teacher calls it "the closure of x". Does this mean the same thing. He also described "closure operations". Is the closure just talking about the subspace formed by the set of points still just like my book?
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Those are not the same thing. A closure (with respect to topology) of a set is not generally a subspace. Closure operations are something more general than either of them. Look at the wikipedia article. – Horstenson Mar 23 '14 at 19:23
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In general, given any operatino $*$, a set $S$ has a closure if $*$ when operated on elements of $S$ (the # of elements of $S$ on which $*$ is operated depends on $*$ itself) gives elements which belong to $S$ itself. I think your teacher called $\langle x\rangle$ the $\bf{closure}$ of $x$ because here we have a Vector space and thus operations $+$ and $.$ on it, so wrt to these operation on $\langle x\rangle$ has closure property.
wanderer
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That make sense, so in this topology, does the closure operations extend or apply to the vector spaces? – cakeyone Mar 24 '14 at 04:08
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I don't know whether you are imposing a topology on your space or not; in general closure in topological space has not the same interpretation, e.g., in a topology the closure is not generally a subspace. – wanderer Mar 24 '14 at 05:44