hello,(adsbygoogle = window.adsbygoogle || []).push({});

i have a clarification question:

if i have a metrizable space, can any open set be written as acountableunion of basis elts?

if not, can it have some properties that make this assertion true, like being T1 or sth like that.

thanks a lot.

just to clarify why i think so, i have a space X with a topology T on it.

Let's say this topology is metrizable, with a metric d. Then, the open sets O(x,r) = {y in X , d(x,y)<r} form a basis for this topology. so any elt in this topology, t in T can be written as a countable union of such O's.

I just want to know if this is works.

thx.

**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!

# Metrizable space

Loading...

Similar Threads - Metrizable space | Date |
---|---|

I Coordinate systems vs. Euclidean space | Dec 4, 2017 |

I Definition of tangent space: why germs? | Oct 2, 2017 |

The Bing metrization theorem | Dec 31, 2010 |

Question about the Nagata-Smirnov metrization theorem | Dec 30, 2010 |

A question about the Urysohn metrization theorem | Dec 13, 2010 |

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