Difference between revisions of "Thread"
From Encyclopedia of Mathematics
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| − | ''of an inverse spectrum | + | {{TEX|done}} |
| + | ''of an inverse spectrum $\{X_\alpha,\omega_\alpha^\beta:\alpha\in\mathfrak A\}$'' | ||
| − | A system | + | 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 $\beta>\alpha$. |
Latest revision as of 17:16, 28 November 2018
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
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