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).

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