members_open

std.topology.members_open · Level L1

Whether every member of a finite family B is an open set of the topology τ, as 1 or 0.

B ⊆ τ

Signature

members_open(tau: f64[m, n], B: f64[c, 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 every row of B among the rows of τ 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

—

Called by

sigma_algebra_axioms is_basis_for is_open_cover

sha256:115cadf47504be22f09e844a7128f6fb496b9b82c03f73908675d58dfbf19ea0

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.members_open · Ω:members_open
Pins: sha256:4ccef3649962f5f8af69c957d484d2855a87fc042295d0ca1f093a593f5c66dathis graph alone
Evidence: sha256:b4eb34a9e9bca383ae0ca11f7a2cfcab17bfe3bec4d807f20159e21d43b1f911the 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.