ISP stands for "internet service provider", and email is, clearly, an "internet service". Unless you run your own server you'll therefore be dependent on an ISP for email service; and even if you do run your own server you'll still be dependent on an ISP for DNS - there is no way to have an email service that isn't in some way dependent on an ISP.
Any email address with the name of an ISP in it is clearly tied to that ISP, in that if you choose to stop using Google, for example, your Google email address will stop working.
If you want an "e-email account that is not tied to an ISP", as you request, then there are two basic options.
(1) Register a domain name, and choose an ISP to handle your email for you. You are at any given moment dependent on this ISP for service, but if you ever get pissed off with them you are not tied to them as you can move your account to someone else whilst keeping the same domain name and email address.
This option does not however meet your "free" criterion, so let's look at the second one:
(2) Look around all the organisations to which you belong, such as professional associations or the university you went to, and see if you can find one offering a "free email for life" redirection service - many do. Sign up to this service, and point your email address at another ISP-dependent email address. So, you might have
[email protected] redirected to
[email protected]. You are not tied to the ISP favourite.free.web.mail.com here, because if you get pissed off with them and move to a different free webmail provider you just go back to mycollege.ac.uk and change the redirection.
So, with this approach, if you find you don't like whichever of Google, Yahoo, Lycos, Hotmail, etc, you initially pick, you can switch to another one without changing your email address.
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Pretty well any email setup meets your "can use wherever she can access a wireless connection" criterion. Email accounts that come "free" with your connectivity provider (BT, Virgin etc) can be used regardless of whether you are connecting via that ISP's wires or not. The only issue is that if you're using POP3 rather than a web mail interface you'll generally have to find out the SMTP server belonging to the wireless access point if you want to send mail (this is usually straightforward).