Share
Explore BrainMass

Path components

(See attached file for full problem description with proper symbols and equations)

---
Let X be a topological space. Mapping a point to the path component which contains x establishes a map .
Show that for any continuous map between topological spaces, there exists a map such that the following holds:
?
? for two continuous maps and we have
? for the identity we have where the latter map denotes the identity on .
---

Attachments

Solution Summary

This solution is comprised of a detailed explanation to show that for any continuous map between topological spaces, there exists a map such that the following holds:
?
? for two continuous maps and we have
? for the identity we have where the latter map denotes the identity on .

$2.19