# Normal Space

Let be a topological space and and are disjoint closed subsets of , then is said to be normal space if there exist open sets and such that , .

In other words, a topological space is said to be a normal space if for any disjoint pair of closed sets and there exist open sets and such that , .

**Remarks**

• The collection of open sets separating the closed sets is called axiom-.

• It may be noted that some topologists consider the normal space basically as well, while others do not.

• Every discrete space contains at least two elements in a normal space.

• Every metric space is a normal space.

T4-Space

A normal space is called a space.

**Theorems**

• Every closed subspace of a normal space is a normal space.

• A closed continuous image of a normal space is normal.

• A topological space is normal if and only if for any closed set and an open set containing , there is at least one open set containing such that .

• Every closed subspace of a space is a space.

• Every and normal space is a regular space.

• If is a normal space and is a closed continuous function from onto a topological space , then is normal as well.