1) Band 2) Banding 3) Fedora accessory 4) Stripe 5) Trilby circlet 
• (n.) A band round the crown of a hat; sometimes, a band of black cloth, crape, etc., worn as a badge of mourning.
Hat'band` (hăt'bănd`) noun A band round the crown of a hat; sometimes, a band of black cloth, crape, etc., worn as a badge of mourning. 
[n] - a band around the crown of a hat just above the brim
noun a band around the crown of a hat just above the brim