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[edit]

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[edit]

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

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