# constant mapping

## constant mapping

Some TCP software constructs the destination Ethernet address from the top 24 bits of the Ethernet address followed by the low 24 bits of the (class A) destination Internet address. For this scheme the top 24 bits of the Ethernet address must be the same on all hosts on the net. Contrast ARP.
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If, in Theorem 10, we assume that f(x) = u [member of] C, a constant mapping, then we get the following corollary.
(Lemma 3.1) Let K : D [right arrow] comp A be a continuous multifunction and v : D [right arrow] [R.sup.n] be a piecewise constant mapping such that d (v (x, y, z), K (x, y, z)) < [rho] for every (x, y, z) [member of] D.
We shall construct, for every n [greater than or equal to] 1, a continuous mapping [g.sup.n] : K [right arrow] [L.sup.1] (D; [R.sup.n]) such that, for every u [member of] K, [g.sup.n] (u) is a piecewise constant mapping of D into A which satisfies, at every (x, y, z) [member of] D,
there exists a piecewise constant mapping [v.sup.n.sub.m] : D [right arrow] A and a point [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] such that, at every (x, y, z) [member of] D,
a piecewise constant mapping [v.sup.p+1.sub.(m,s)] : D [right arrow] A which satisfies, at every (x, y, z) [member of] D,
(P2): For [for all] (a, i) [member of] [S.sub.[alpha]], (b, j) [member of] [S.sub.[beta], we consider the following situation separately: ([[gamma].sup.(a,i).sub.[alpha],[alpha]) ([[gamma].sup.(a,i).sub.[beta],[beta]) is a constant mapping on [[LAMBDA].sub.[alpha]] and we denote the constant value by
(b) If [alpha],[beta],[delta], [member of] Y with [alpha],[beta][greater than or equal to] [delta] ([[gamma].sup.(a,i).sub.[alpha],[alpha]) ([[gamma].sup.(a,i).sub.[beta],[beta]) is a constant mapping on [[LAMBDA].sub.[alpha]] = k, then, ([[gamma].sup.(a,i).sub.[alpha],[alpha]) ([[gamma].sup.(a,i).sub.[beta],[beta]) = k, then ([[gamma].sup.(ab,k).sub.[alpha],[beta][delta])
Fisher, "Fixed point and constant mappings on metric spaces," Atti della Accademia Nazionale dei Lincei.

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