So, in the topology text I'm reading is mentioned that if each ##X_n## is first countable, then ##\prod_{n\in \mathbb{N}} X_n## is first countable as well under the product topology. And then it says that this does not need to be true for the box topology. But there is no justification at all. Does anybody know a good counterexample?(adsbygoogle = window.adsbygoogle || []).push({});

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Box topology does not preserve first countable

Loading...

Similar Threads - topology does preserve | Date |
---|---|

I Turning the square into a circle | Feb 16, 2018 |

I Ordered lattice of topologies on the 3 point set | Dec 13, 2017 |

What does vanishing at infinity mean for a topological space? | Oct 3, 2013 |

Does this form a topology? | Feb 27, 2012 |

[topology] new kind of separation axiom? where does it fit in? | Dec 25, 2011 |

**Physics Forums - The Fusion of Science and Community**