is_homeomorphism

std.topology.is_homeomorphism · Level L3

Whether a map f between finite spaces is a homeomorphism, as 1 or 0: a bijection that is continuous and whose inverse is continuous, which for a bijection means the image of every open set is open. A homeomorphism preserves the topology only: not distances, angles or smoothness.

f bijective, f and f⁻¹ continuous

Signature

is_homeomorphism(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 a permutation, preimages open and images open 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_continuous

Called by

—

sha256:266bc1e678c5ae273a6f1737bafe485e24cc51f96b5182139a5c91390e09b24a

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_homeomorphism · Ω:is_homeomorphism
Pins: sha256:1158aded69399bb025addee665ed2c315f3ec1c0a6175dcaf82c59ba6402b434this graph and the 1 it reaches through calls
Evidence: sha256:db43791537cb18ff559cf7b4a472691dc9ae3211abd64e39c418395d11ab6316the 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.