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April 1, 2013 / porton

A new simple proposition about generalized limits

I’ve added the following almost trivial proposition to the draft of my book “Algebraic General Topology. Volume 1”:

Proposition \tau \left( y \right) = \mathrm{xlim}\, \left( \left\langle \mu \right\rangle^{\ast} \left\{ x \right\} \times^{\mathsf{FCD}} \uparrow^{\mathrm{Base}\, \left( \mathrm{dom}\, \nu \right)} \left\{ y \right\} \right) (for every x). Informally: Every \tau \left( y \right) is a generalized limit of a constant funcoid.

Note that \tau is the function which transforms from simple numbers to values of generalized limits.

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