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Year 2 of the mathematics course of the University of Oxford

Options II course of the University of Oxford

Past exam of the options II course of the University of Oxford

2012

An <accumulation point> of $A$ is a point $x\in X$ such that every <open neighbourhood> of $x$ contains a point of $A$ different from $x$:
$$
\boxed{x\in A'\iff (U\setminus\{x\})\cap A\neq\varnothing\text{ for every open }U\ni x.}
$$
The point itself need not belong to $A$. Requiring a different point distinguishes accumulation from mere membership in the <closure>.

Solution

Past exam of the options II course of the University of Oxford / 2012 / E / E3 / a / iv / Solution

Past exam of the options II course of the University of Oxford / 2012 / E / E3 / a / iv / Solution

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Past exam of the options II course of the University of Oxford / 2012 / E / E3 / a / iv / Solution

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