Just a small (and, really, quite useless) little nugget here:(adsbygoogle = window.adsbygoogle || []).push({});

In the definition of a topological space, we require that arbitrary unions and finite intersections of open sets are open. We also need that the whole space and the empty set are also open sets.

However, this last condition is actually redundant - the empty union is empty and, in the context of subsets of some set, the empty intersection is the whole set, so that the whole space and the empty set are open is actually implied by the first two properties!

Of course, I wouldn't suggest not including the last condition in the definition when teaching topology, just thought it was interesting to point out :)

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

# Definition of a Topological Space

Have something to add?

- Similar discussions for: Definition of a Topological Space

Loading...

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