I keep wanting to call it a "space" but that conflicts with the 2-space, 3-space, 4-space, n-space nomenclature.
e.g., in 3-space, you can hold one variable constant to get a 2-space "slice" (a plane) of the 3-space object. e.g. if I have $x^2 + y^2 + z^2 = 1$ (a sphere), I can take $z=0$ which gives me a plane slice (the x-y plane) on which is a circle of radius 1.
In 4-space, if I have $e_1^2 + e_2^2 + e_3^2 + e_4^2 = 1$ (a 4-sphere), I can take $e_4=0$ to give me a [XXX] slice (the x-y-z [XXX]) in which is a sphere of radius 1.
What is XXX?