Topospaces, The Topology Wiki (pre-pre-alpha)

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From Topospaces

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space
View a complete list of properties of topological spaces

This is a variation of normal space
View other variations of normal space | read a survey article on varying normal space

Contents 1 Definition 1.1 Symbol-free definition 2 Relation with other properties 2.1 Stronger properties 2.2 Weaker properties 3 References 3.1 Textbook references

Definition

Symbol-free definition

A topological space is termed binormal if its product with the unit interval (with the product topology) is a normal space.

Equivalently (??), a topological space is termed binormal if it is both a normal space and a countably paracompact space.

Relation with other properties

Stronger properties

property	quick description	proof of implication	proof of strictness (reverse implication failure)	intermediate notions
Compact Hausdorff space
Paracompact Hausdorff space

Weaker properties

property	quick description	proof of implication	proof of strictness (reverse implication failure)	intermediate notions
Normal space

References

Textbook references

• Algebraic Topology by Edwin H. Spanier^{More info}, Page 56, Exercise B-2 (definition introduced in exercise)