is_neighborhood

std.topology.is_neighborhood · Level L3

Whether a subset N is a neighbourhood of the point x in a finite topology, as 1 or 0: some open U has x ∈ U ⊆ N, that is, x lies in the interior of N. A neighbourhood need not be open.

∃U ∈ τ: x ∈ U ⊆ N

Signature

is_neighborhood(tau: f64[m, n], x: f64[], N: f64[n]) → f64[]

Structure

The function as NOVA stores it: one box per input, operation and output, and arrows that carry values. A double border marks another library function this one runs — called once, or by Scan once per element; select it to open that function.

input
operation
constant
call
output

Verification

Signature proven by NOVA’s shape solver, for every size.
Equal to the reference x in the interior of N in exact rational arithmetic, on all 40 test cases.
All 40 float64 results are exact: the error is zero.
Interpreter and NumPy backend return bit-identical results.
At float32 too: the 40 test cases rounded to float32, and 40 of them exact, with zero error.

Accuracy in detail

correctly rounded (the float64 nearest the exact value): 100%
bit-equal to the NumPy formula in float64: 100%
largest error, in units in the last place: 0

Identity

Calls

interior

Called by

—

sha256:badcf04472a131f533567a38f8f8b942c520adf9edf22fd8b6c4adb02d5a9c85

The semantic hash of the graph. It changes when the program changes, and never when only its documentation does.

Control handle

Symbol: Ω:std.topology.is_neighborhood · Ω:is_neighborhood
Pins: sha256:e7f15abfcff238adb5a5d3c4aa238230dbbd9d300a2f340cd76df2323f793f6cthis graph and the 1 it reaches through calls
Evidence: sha256:6f5d97b30f6442c102b59f0f67213e4bba2a6472552846e52813761f57aa5d69the hash of its verification record
Needs: no capability: a pure function

Through NOVA’s control layer, the symbol launches this function only while the program still matches what it pins: a change to this graph, or to any graph it reaches, needs a migration first.