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"built up" is a perfectly acceptable phrase in written English.
You can use it to describe gradual progress or development over time, such as in the sentence: After years of hard work, his business had gradually been built up into a successful enterprise.
Dictionary
built up
verb
Past of build up
Exact(56)
They built up a rapport.
It had built up sharply.
Next she built up virtuosity.
They are built up step by step.
Canvasses are built up in collaged layers.
"Everything just built up," Glover said.
"It was all built up," he said.
Similar(4)
The model considers four built-up classes: non built-up, low-density, medium-density and high-density built-up.
Seven-storey building in built-up area.
The positive grades mean the built-up scenes, while negative values the non-built-up ones.
The training database contains only clearly built-up and non-built-up pictures.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com