# Bound-narrowing trajectory

*This article defines a property that can be evaluated for a trajectory on the space of functions on a manifold*

## Definition

Let be a manifold and be a function , where:

- denotes the time parameter, and varies in
- denotes the spatial parameter, and varies in

In other words, is a trajectory (or path) in the space of all functions from to .

Then, is said to be **bound-narrowing** if it is both max-decreasing and min-increasing or equivalently if it satisfies the following condition: