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Coaster, maybe, with a bit out of the mast? (3)

Ross

I believe the answer is:

mat

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'the mast?' is the definition.
The definition and answer can be both man-made objects as well as being singular nouns.
Maybe you can see an association between them that I don't see?

'coaster maybe with a bit out' is the wordplay.
'coaster maybe' becomes 'm' (I can't explain this - if you can you should believe this answer much more).
'with' says to put letters next to each other.
'a bit' becomes 'ate' ('bite' can be similar in meaning to 'eat').
'out' means to remove the last letter.
'ate' with its last letter removed is 'at'.
'm'+'at'='MAT'

'of' is the link.

Can you help me to learn more?

(Other definitions for mat that I've seen before include "Foot-wiper on which welcome may be kept" , "Small carpet" , "A piece of material as floor covering" , "Piece of material for wiping feet on" , "Rug; without a shine" .)

I've seen this clue in the Evening Standard.
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