# Fibre product

*of a system of topological spaces with respect to a system of continuous mappings , *

The subset of the Tikhonov product , which is considered in the induced topology and which consists of the points for which , for all indices and from . The mapping which brings the point into correspondence with the point (or with the point ) is called a projection of the fibre product onto , (or onto ). If the space is a one-point space, then . If the , , are completely-regular spaces, the fibre product is completely regular. The fibre product, in particular its special case the partial product, is well suited for the construction of universal (in the sense of homeomorphic inclusion) topological spaces of given weight and given dimension (cf. Universal space).

#### Comments

In category theory the term "pullbackpullback" is also used, cf. Fibre product of objects in a category.

**How to Cite This Entry:**

Fibre product.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Fibre_product&oldid=17578