# Thread

From Encyclopedia of Mathematics

*of an inverse spectrum $\{X_\alpha,\omega_\alpha^\beta:\alpha\in\mathfrak A\}$*

A system $x=\{x_\alpha\}$ of points $x_\alpha\in X_\alpha$ (one point from every $X_\alpha$), that is, a point of the product $\prod_{\alpha\in\mathfrak A}X_\alpha$ of the sets $X_\alpha$, such that $\omega_\alpha^\beta(x_\beta)=x_\alpha$ whenever $\beta>\alpha$.

#### Comments

The sets of threads of an inverse spectrum (or projective system, or inverse system) is called the (projective, inverse) limit of that spectrum (see the editorial comments to Limit).

#### References

[a1] | R. Engelking, "General topology" , Heldermann (1989) |

**How to Cite This Entry:**

Thread.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Thread&oldid=43500

This article was adapted from an original article by B.A. Pasynkov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article