The quality or state of being glazy; the characteristic of having a smooth, glass-like, or lustrous appearance.
From 'glazy' plus the noun-forming suffix -ness, which converts adjectives into abstract nouns describing their qualities. This is a standard English derivation pattern.
The glaziness of a pottery piece determines its water-resistance and durability—potters discovered centuries ago that the glassier something looks, the better it holds liquids, which is why ceramic containers evolved their distinctive shine.
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