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Given a point $x$ in a topological space, let $N_x$ denote the set of all neighbourhoods containing $x$. Then $N_x$ is a directed set, where the direction is given by reverse inclusion, so that $S ≥ T$ if and only if $S$ is contained in $T$. For $S$ in $N_x$, let $x_S$ be a point in $S$. Then $(x_S)$ is a net. As $S$ increases with respect to $≥$, the points $x_S$ in the net are constrained to lie in decreasing neighbourhoods of $x$, so intuitively speaking, we are led to the idea that $x_S$ must tend towards $x$ in some sense.

I wonder if its only for fun :D

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    The idea of a net is to generalize the notion of sequence convergence to something more powerful. Had they directed by inclusion, then moving along the net corresponds to a *less* tight focus around $x$, which is really going the wrong way if we want to talk about the $x_S$ tending toward $x$ in any reasonable sense.2012-05-24
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    @CameronBuie but even i can use inclusion and formulate the same notion isn't it with respective change ? Am i missing something here ?2012-05-24
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    I've posted an example as an answer. Hopefully it helps clear things up, but let me know.2012-05-24

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