My textbook is indicating to me that sometimes {x \in X : a <= x <= b} is an open set. How can this happen?(adsbygoogle = window.adsbygoogle || []).push({});

My only guess is that if X has a smallest and largest element, called a and b, then sure. Otherwise?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

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

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

# Is [a,b] ever an open set in the order topology?

**Physics Forums | Science Articles, Homework Help, Discussion**