- E1
[0J1] Prerequisites:[252].Let \(X\) be a set and \({\mathcal V}β {\mathcal P}(X)\) a family of parts of \(X\); we define \(π\) as the intersection of all topologies that contain \(\mathcal V\) i.e.
\[ π{\stackrel{.}{=}}\underlineβ\{ π, πβ \mathcal V, π \text{~ topology in ~ }X\} \]Show that \(π\) is a topology.
\(π\) is the βtopology generated by \(\mathcal V\)β; it is also called βthe smallest topology that contains \(\mathcal V\)β.
EDB β 0J1
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Authors:
"Mennucci , Andrea C. G."
.
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