---
date: 2022-04-01 20:52
modification date: Friday 1st April 2022 20:52:57
title: "CW complex"
aliases: [CW complex, "CW-complex", CW approximation, CW]

---

Last modified date: <%+ tp.file.last_modified_date() %>


---

- Tags 
	- #todo/untagged
- Refs:
	- #todo/add-references
- Links:
	- [Serre fibration](Unsorted/Serre%20fibration.md)
	- [Obstruction theory in homotopy](Unsorted/Obstruction%20theory%20in%20homotopy.md)
	- [Hurewicz](Unsorted/Hurewicz.md)
	- 

---

# CW complex
![](attachments/Pasted%20image%2020220401205304.png)

Attachment:
![](attachments/Pasted%20image%2020220422155916.png)
![](attachments/Pasted%20image%2020220422155953.png)

# Statement and proof of CW approximation

![](attachments/Pasted%20image%2020220401211618.png)
![](attachments/Pasted%20image%2020220401211637.png)

![](attachments/Pasted%20image%2020220401211651.png)

# Passing to limits
![](attachments/Pasted%20image%2020220401212022.png)
![](attachments/Pasted%20image%2020220401212453.png)
![](attachments/Pasted%20image%2020220401212513.png)

See [Eckman-Hilton](Eckman-Hilton).

# Applications

For [Postnikov towers](Unsorted/Obstruction%20theory%20in%20homotopy.md):
![](attachments/Pasted%20image%2020220401212336.png)
![](attachments/Pasted%20image%2020220401212344.png)

# With G actions

![](attachments/Pasted%20image%2020220403175319.png)