Web based email doesn't work in nearly the same way. Web based email using some sort of scripting language, and an on-server storage backend to display your messages. There's no standard protocol for that sort of thing, so you won't be able to do it "easily". Also, you don't need to download your whole inbox, generally just messages from the last x days.
But you probably know both of the things I just mentioned, so I'm out of ideas.
Michael
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