Elliot Haughin twitter library, stay log in after the browser is closed and reopen?

[eluser]searain[/eluser]
I installed Elliot Haughin's twitter library. and It works.

http://www.mysite.com/tweet_test

It got me to the twitter authorize page
http://api.twitter.com/oauth/authorize...

After I authorize it, and then revisit http://www.mysite.com/tweet_test, it will generate "hi there". That means the access to my twitter account through this app url is authorized already.

Everything is fine so far.

But then I closed my browsers, and then revisited http://www.mysite.com/tweet_test, instead of getting me to the twitter authorize page again, it gave me "hi there" directly, that means I am still authorized to access my twitter account through this url? That makes me worry.

That means I am still authorized to access my twitter account through this app url, http://www.mysite.com/tweet_test, even the browser was closed and reopen.

Now my questions are

1) if some app like this, the first user authorizes it, and closes it. Thinking his account is safe.
2) the second user comes to this computer, opens the browser, goes to the same app page, he get accesses to the first user's account through this app?

How twitter api allows this? That means, once you allow an app access to your account, you open your account to this app's url when next user comes to the same computer visit the same url?

I must miss something here.


Thanks!