alice/topology/
maps.rs

1use alloc::boxed::Box;
2use alloc::collections::BTreeSet;
3use crate::core::morphism::Morphism;
4use crate::topology::space::TopologicalSpace;
5
6pub struct ContinuousMap<X, Y>
7where
8    X: TopologicalSpace,
9    Y: TopologicalSpace,
10{
11    f: Box<dyn Fn(&X::Point) -> Y::Point + Send + Sync>,
12}
13
14impl<X, Y> ContinuousMap<X, Y>
15where
16    X: TopologicalSpace,
17    Y: TopologicalSpace,
18{
19    pub fn new<F>(f: F) -> Self
20    where
21        F: Fn(&X::Point) -> Y::Point + Send + Sync + 'static,
22    {
23        Self { f: Box::new(f) }
24    }
25
26    pub fn apply(&self, p: &X::Point) -> Y::Point {
27        (self.f)(p)
28    }
29
30    pub fn preimage(
31        &self,
32        domain_points: &BTreeSet<X::Point>,
33        open_set: &BTreeSet<Y::Point>,
34    ) -> BTreeSet<X::Point>
35    where
36        X::Point: Ord,
37        Y::Point: Ord,
38    {
39        domain_points
40            .iter()
41            .filter(|p| open_set.contains(&self.apply(p)))
42            .cloned()
43            .collect()
44    }
45
46    pub fn is_continuous_on(
47        &self,
48        domain: &X,
49        codomain: &Y,
50        domain_points: &BTreeSet<X::Point>,
51    ) -> bool
52    where
53        X::Point: Ord,
54        Y::Point: Ord,
55        Y: OpenSetsIter,
56    {
57        for open in codomain.open_sets_iter() {
58            let pre = self.preimage(domain_points, &open);
59            if !domain.is_open(&pre) {
60                return false;
61            }
62        }
63        true
64    }
65}
66
67impl<X, Y> Morphism for ContinuousMap<X, Y>
68where
69    X: TopologicalSpace,
70    Y: TopologicalSpace,
71    X::Point: Clone,
72    Y::Point: Clone,
73{
74    type Domain = X::Point;
75    type Codomain = Y::Point;
76
77    fn apply(&self, x: &X::Point) -> Y::Point {
78        (self.f)(x)
79    }
80}
81
82pub trait OpenSetsIter: TopologicalSpace {
83    fn open_sets_iter(&self) -> alloc::vec::IntoIter<BTreeSet<Self::Point>>;
84}
85
86use crate::topology::space::FiniteTopologicalSpace;
87
88impl<P: Clone + Eq + Ord> OpenSetsIter for FiniteTopologicalSpace<P> {
89    fn open_sets_iter(&self) -> alloc::vec::IntoIter<BTreeSet<P>> {
90        self.open_sets().iter().cloned().collect::<alloc::vec::Vec<_>>().into_iter()
91    }
92}
alice/topology/maps.rs

alice/topology/
maps.rs
