is_continuous

std.topology.is_continuous · Level L3

Whether a map f from a finite space (X, τ_X) to (Y, τ_Y) is continuous, as 1 or 0: the preimage f⁻¹(V) of every open V of Y is open in X. It is the preimage that must be open; images of open sets need not be.

V ∈ τ_Y ⇒ f⁻¹(V) ∈ τ_X

Signature

is_continuous(tauX: f64[m, n], tauY: f64[p, k], f: i64[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 preimage among the open sets of X 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

is_measurable is_homeomorphism

sha256:f5ed8abf4a5e2399598d106ef257f1203eab12c780706a0e2a112beea9be9b6e

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_continuous · Ω:is_continuous
Pins: sha256:5cc151bb009272dabfd7fae8b9122b42e3998bc4ff19fd8f189e428257c8294athis graph alone
Evidence: sha256:ca78b20f464870621e4d7a786b263544dee115176aa4f28660fe282c97998770the 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.