is_open_cover

std.topology.is_open_cover · Level L1

Whether a finite family C (one set per row) is an open cover of the subset K in the topology τ: whether every member is open, and whether the members together contain K, each as 1 or 0. A finite space is compact, since its topology itself is finite, so every open cover has a finite subcover; one cover checked does not by itself prove compactness.

C ⊆ τ, K ⊆ ∪C

Signature

is_open_cover(tau: f64[m, n], C: f64[c, n], K: f64[n]) → f64[], 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 rows of C among τ, and K inside their union in exact rational arithmetic, on all 40 test cases.
All 80 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

members_open

Called by

—

sha256:7b23bf9ed3097c3d304ed1872fcdaff7f534f29fe393dcf9e8a74a8b96a24ab0

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_open_cover · Ω:is_open_cover
Pins: sha256:7a9ef3d34d150ba292ec2e69bc1a00540338ef8ed623d7d2792155dc5f2aa0dethis graph and the 1 it reaches through calls
Evidence: sha256:291d518561e4e26a387bb8adbca0d660ca2a0e2e9f5df0718fbd8930f7dcf3a4the 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.