under the impression
Believing or making assumptions, often incorrectly.
We opened a store in Beijing under the impression that our product would be popular.
impression
UK /ɪmˈpɹɛʃn̩/ US /ɪmˈpɹɛʃn̩/
noun 5verb 1
Definitions
noun
1
The indentation or depression made by the pressure of one object on or into another.
His head made an impression on the pillow.
2
The overall effect of something, e.g., on a person.
He tried to make a good impression on his parents.
Their empires, triumphs, conquests, and projects, have left little impression behind them, notwithstanding the attention they once attracted, and the violent convulsions which they caused in the state of the world.
3
A vague recalling of an event, a belief.
I have the impression that he's already left for Paris.
4
An impersonation, an imitation of the mannerisms of another individual.
5
An outward appearance.
verb
1
To manipulate a blank key within a lock so as to mark it with impressions of the shape of the lock, which facilitates creation of a duplicate key.
The trick in impressioning a key is to remove only a small amount of the blank, by filing or cutting, from the pin positions where impressions have been left.
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