Assuming one is inside an [eruv][1] which generally permits transferring between domains on Shabbat, may one use an umbrella on Shabbat? If not, *why* not?

---

Follow-up question: What about other things that fold up/out (e.g. strollers, portable chairs, tables, or an [extendable canopy][2])?

  [1]: http://en.wikipedia.org/wiki/Eruv
  [2]: http://retractablecanopies.tumblr.com