subspace_topology

std.topology.subspace_topology · Level L0

The subspace topology on a subset Y: τ_Y = {U ∩ Y : U ∈ τ}, one row for each open set of τ (rows may repeat; the family is the set of rows). A relatively open set need not be open in X.

τ_Y = {U ∩ Y : U ∈ τ}

Signature

subspace_topology(tau: f64[m, n], Y: f64[n]) → f64[m, n]

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 each row times Y in exact rational arithmetic, on all 40 test cases.
All 707 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

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sha256:9c05c4968889472099344e3dc82d016e033a8117462a78beb953d7ea18e44e74

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.subspace_topology · Ω:subspace_topology
Pins: sha256:8333979c9466daf388f389975e18748ac5104713375137defad668f7b87a5226this graph alone
Evidence: sha256:a1479cd477427c023bb19bca8d0437e074c3b125c326a0de0dda0b9cb147e442the 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.