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When you're viewing the AI in Preview, you see an expanded version of the tracing. It consists of a lot of single shapes joining each other. And because every single one of the shapes is kind of smoothed at its edges, there are those little white gaps. This doesn't matter when printing, but you see it on your screen. You could consider converting your live trace into pixels in Illustrator and then exporting it (just for the prupose of viewing it in Preview or sending it to your friends). For printing you keep the vector version.
For converting into pixels choose Object > Rasterize
Thanks for helping me out here. I really appreciate it. I do have some further questioning though if you wouldn't mind. I'm just trying to understand what's happening.
In Illustrator, I can zoom in and in and in to these lovely vector graphics and not see any white lines between the shades/colours. So how come when I view the saved file in Preview at half the size I see the lines?
I followed your suggestion and rasterized it and the lines don't appear. I haver to admit I'm a bit disappointed however as I really wanted the smooth vector drawings. If ultimately that is the effect I want to get, and I want to avoid the white lines due the pictures being displayed mainly on my computer, what advice might you give me to get there?
Very much appreciated,
as long as the traced image is inside Illustrator and you haven't hit the "Expand"-button, this is a live object and it's treated differently when drawn on screen.
When you save the file as AI, this file normally includes a PDF part and in this PDF part the "live trace" gets expanded automatically (is no more live and so gets separated in single objects with those white lines). When you open the AI file in Preview, Preview shows the PDF part as it can't open native AI and shows the expanded object.
Those white lines won't be visible in print, but on screen. They are caused just by the feature that makes vector images look good on screen: antialiasing, which is smoothing the objects' edges.
So unfortunately you can't have both.
Monika, thanks again! At least I understand now and can get on with it..!
You could select the whole piece of art and go to Effect>Path>Offset path, enter a small value like 1px.