is_closed

std.topology.is_closed · Level L1

Whether a subset A is closed in a finite topology, as 1 or 0: its complement X \ A is open. Open and closed are not opposites: ∅ and X are both, and a set may be neither.

[X \ A ∈ τ]

Signature

is_closed(tau: f64[m, n], A: 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 the complement among the rows 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

is_open

Called by

—

sha256:5fdf09f47468dc6f32c079bf661c87663e1d1c223e9cca3b8efe03cc9b433cc8

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_closed · Ω:is_closed
Pins: sha256:dad20c05bcac88310a7ed3cee06cc66d65fa2d8a698509fde2b09e40a63d27cbthis graph and the 1 it reaches through calls
Evidence: sha256:68593e89ef1178ffcc8c5e3ab06b7e0ae74b969a7a2e5464d159a2380fa552fdthe 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.