# adjunction space

## Primary tabs

Defines:
adjunction
Type of Math Object:
Definition
Major Section:
Reference

## Mathematics Subject Classification

54B17 no label found

## Comments

### Two comments on adjunction space

1. I have seen in some books this definition with the assumption that A is closed subspace. (Walker: Stone-Cech compactification, p.267; Engelking: General Topology)
I wasn't able to find a reference, where this assumption is relaxed. (But I would say, whenever I've used this notion, the condition of closedness wasn't necessary.)
Do you know about a book where adjunction space is used without this assumption?

2. Perhaps it could be mentioned in the article, that the adjunction space is pushout in the category of topological spaces.