Thread

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)