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In the present paper it is proved that the functors $O_\tau$ of $\tau$-smoothorder preserving functionals and $O_R$ of Radon order preserving functionalspreserve the weight of infinite Tychonoff spaces. Moreover, it is establishedthat the density and the weak density of infinite Tychonoff spaces do notincrease under these functors.

On the weight and the density of the space of order-preserving functionals