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The phrase "an inner space" is correct and usable in written English.
It can be used to refer to a mental, emotional, or spiritual realm within oneself, often in contexts related to introspection or personal growth.
Example: "Meditation allows us to explore an inner space where we can find peace and clarity."
Alternatives: "a personal realm" or "an internal dimension".
Exact(9)
Their alternative was to put shrubs like yews toward the street, where they could grow unclipped and provide privacy for an inner space crammed with surprises like fountains and fine ferns.
It featured an electronic score by Eduard Artemyev but the Melbourne-born Ben Frost has said "it never achieves musically the effect I think Tarkovsky was going for, which was to make a film about an inner space as opposed to an outer one".
It is easy to prove that (W_2^1[a,b]) is an inner space.
It is easy to prove that (W_2^{(1,1)}(D)) is an inner space.
The fact that the subjects and the experimenter may share similar assumptions about the causes of quasi-visual experience (the "folk theory" of images as inner pictures), so that both interpret the experiment in terms of operations on inner pictures in an inner space, is not evidence that those assumptions are correct.
Then (E, < ·, · >) is an inner space with < x, y > = ∑ n ∈ Z [ ( Δ x n, Δ y n ) + ( L ( n ) x n, y n ) ], ∀ x, y ∈ E. and the corresponding norm ∥ x ∥ 2 = ∑ n ∈ Z [ ( Δ x n ) 2 + ( L ( n ) x n, x n ) ], ∀ x ∈ E. Furthermore, we can get that E is a Hilbert space.
Similar(51)
"Space Program: Mars," a collaboration between Sachs, Creative Time and the armory, is an inner-space playground for the whole family.
The formation of such a structural feature that consists of a nanotube with an empty inner space can be used for loading various chemicals, ranging from small molecules to proteins, drugs, biomolecules, and so on.
Designed by Wren's extraordinary pupil, Nicholas Hawksmoor, it exuded early 18th-century elegance, with a dramatic inner space based upon a square within a square, its black columns highlighted by sinuous gold twinings.
The pavilion is characterized by a small inner space with changeable dimensions and an adaptive enclosure.
It does not broadcast its accomplishments for the cosmos but tracks the personal and domestic and local, a harrowed inner space.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com