Math and science::Topology
Connectedness. 4 lemmas
1. The edge of a connected space
Let
If
2. [something of a something on] a connected space is connected
Let
In particular, any quotient of a connected space is connected.
3. The [something] of two connected spaces is connected.
4. A space that has [a particular way of being composed] is connected.
Let
This lemma says that gluing together overlapping connected spaces produces connected spaces.