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Why is the Inspector saying that an indexed color space is used?
Indexation of images is a way of compressing the image without any data loss. Indexing an image will keep the resolution and colorspace intact, but the structure of the image will change. When an image is indexed an index table will be created. This is a list of the different colors that are used. The image itself will contain reference numbers to this index table. Especially when the image uses a lot the same colors, this can save a lot of space. Indexing an image won’t change the way an image looks or will be printed. Each pixel will keep its original color and colorspace.
E.g. a CMYK image is indexed. The index table will contain each color once with its CMYK percentages. Each pixel in the image will contain a single reference to the index table. If this same image wouldn't be indexed, each pixel would have it's CMYK coordinates. If that image would contain 2 pixels with the same CMYK values, this information will be stored twice. If an image uses a lot of different colors, indexing this image will not make decrease the file size. In this case the image will not be indexed.