<div dir="ltr">On Sun, Dec 1, 2013 at 10:24 PM, Martin Escardo <span dir="ltr"><<a href="mailto:m.escardo@cs.bham.ac.uk" target="_blank">m.escardo@cs.bham.ac.uk</a>></span> wrote:<br><div><div class="gmail_extra"><div class="gmail_quote">
<blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex"><div class="im">[...]</div>
Then the problem with the modulus-of-continuity functional is that it<br>
doesn't preserve limits (it is not continuous).<br>
<br></blockquote><div> </div><div>Does this mean that once we fix a modulus of continuity functional M we should be able to find a sequence f_i of continuous functions converging to g such that M f_i doesn't converge to M g? All without assuming M itself to be continuous?<div>
<div class="gmail_extra"><br></div><div class="gmail_extra">It could be an interesting example.</div></div></div><div><br></div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
If you want to know more, please feel free to ask. There are models of<br>
type theory (classical and constructive) based on the above ideas. One<br>
of them is Johnstone's topological topos. A closely related one,<br>
studied by Chuangjie and myself, admits a constructive treatment.<br>
<br></blockquote><div><br></div><div>What's a good article to start from for the constructive model?</div><div><br></div><div><br></div><div>-- Andrea</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left-width:1px;border-left-color:rgb(204,204,204);border-left-style:solid;padding-left:1ex">
Best,<div class=""><div class="h5"><br>
Martin<br>
<br>
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