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I have white polygons on same layer and I want to fill the space around the polygons (i.e. the whole background) with a single black polygon. The result would be a black & white map.

Is there anyway to do it by using rasters instead?

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you can modify the dataframe properties to set a backgroud color. No need to create a new data. Go to dataframe properties (right click on the data frame) > frame and select a background colour = black.

If you need the raster for some reason (but I don't think so), you can convert your polygon to raster: the raster will be no data where you don't have a polygon.

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