What's a simple path?

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What's a simple path? ตอบหน่อย
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ขอพูดคุย กันบ้าง อย่าละเลย
ไยเพื่อนเฉย ชังข้าฯ หรืออย่างไร

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In geometry, a simple path is a simple curve, namely, a continuous injective function from
an interval in the set of real numbers R to R^n or more generally to a metric space or a topological space.

In graph theory a simple path is a path in a graph which
does not have repeating vertices. See path (graph theory).

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In mathematics,
a path in a topological space X is a continuous function f from the unit interval I = [0,1] to X

f : I → X.

The initial point of the path is f(0) and the terminal point is f(1).

One often speaks of a "path from x to y" where x and y are the initial and
terminal points of the path.

Note that a path is not just a subset of X which "looks like" a curve,
it also includes a parameterization.