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A Levi subgroup appears in a group version of a Levi decomposition. A Levi subgroup is a reductive complement to the unipotent radical of a parabolic subgroup.

RSW rectangle crossings and positive association join two separated one-arm events with probability bounded below uniformly over scale.

This is the elliptic-curve specialization of the Néron–Tate height. For an associated logarithmic projective height $h$, one normalization is $\hat{h}(P)={\lim }_{no\infty }{4}^{-n}h([2^n]P)$.

The canonical height isIt is a quadratic form, vanishes on torsion points, and satisfies $\hat{h}(\varphi P)=\mathrm{deg}(\varphi )\hat{h}(P)$ for every isogeny $\varphi$.

The map is a connecting homomorphism from the multiplication exact sequence. Its image is constrained by the local conditions defining the Selmer group of an elliptic curve.

The multiplication-by-$n$ sequence gives an injective connecting mapLocal conditions restrict its image to the finite $n$-Selmer group.

For $A\to B\to C=B/I$, there is a right-exact sequencewhere $[i]\mapsto di\otimes 1$ and $db\otimes c\mapsto cd\bar{b}$.

Every word in simple Coxeter generators can be reduced by braid moves and cancellations $ss\mapsto 1$. Consequently, a word is reduced exactly when no sequence of braid moves can make a cancellation possible.

In equilibrium, a Bernoulli-feedback $M/M/1$ queue has the same queue-length process as an ordinary queue with service rate $\mu (1-p)$, so its external departures form a Poisson process of rate $\lambda$.

An open map sends every open subset of its source to an open subset of its target. This is an image property; continuity instead concerns preimages of open sets. A local diffeomorphism has both properties, but openness alone does not promise unique recovery of an input. In the periodic coordinate map under the inverse function theorem, open patches give open output regions while multiple angle values still give the same output.

Together, open and closed maps describe the two image-set preservation properties.