Lightroom opens images in a proPhoto workspace, and it is not changeable or selectable. If you are shooting raw, choosing a different color space in your camera settings isn't going to have any impact on what you see in Lightroom. When you export copies of your images you can export them in Adobe RGB or sRGB, but Lightroom itself works in the widest color space.
If the image is a camera JPG, then many cameras substitute an underscore for the first character of the filename (this is I think in the standards of the digital camera manufacturer's association) when the camera is set to AdobeRGB. This is not present when pictures are taken with the camera set to SRGB.
This information is not relevant for camera Raw, but at least some cameras will in fact repeat this same naming convention, for those as well.
I don't recall that this information is readily accessible, for derived files which have been assigned a colourspace when created for external editing. It is possible to make external editing presets, but IIRC the standard file suffix (such as, "XXXXX-edit.XXX") is not set separately by these. In the case where a file is sent to Photoshop in an as yet unsaved state, one could when saving it, modify the file name to denote the colourspace.
However, I am not sure how useful that would be from the LR end.
If you would have liked a file to be in a big colourspace, but it has previously been saved in a small colourspace, then there's little you can now do about that. If you would have liked it to be in a small colourspace - you simply select that when exporting.
You simply don't need to bother about a file's colourspace or bit depth otherwise. LR takes care of making best use, of whatever is there.
Here are two ways:
1. Use a smart collection, and have a rule for each possible colorspace.
(the item name is: 'Color / Source Color Profile')
2. Use ExifMeta plugin (free, by me).
thank you Rob!
I am really surprised to see that Lightroom doesn't show the full range of metadata.
Why should I go the bridge to see this little but very vital piece of data of a picture "cmyk" or "rgb"