Definition talk:Topology Generated by Synthetic Sub-Basis

I understand your use of $$:=$$ meaning (I think) "is defined as", but what is $$=:$$? --Matt Westwood 07:34, 26 January 2010 (UTC)


 * As far as i know, $$:$$ separates a name from the thing it is defined to refer to, and $$:$$ is followed by how the name refers to the object. So $$a := b$$ means that whenever I say $$a$$, I mean the same object as if I had said $$b$$. I could also say $$a :\Leftrightarrow b$$, this would mean that whenever I say $$a$$, I refer to something that is equivalent to $$b$$ (whatever that means in the surrounding context). Same goes for things like $$f : X \rightarrow Y$$ and so on. I'm not sure if this is standard in any way (it's just how I learned it). If there's some established standard around here, just let me know.


 * And switching it around like $$y =: x$$ is just the same as saying $$x := y$$. Sometimes it's more readable: Whereas $$x := y$$ is like "I will use the name $$x$$ for the following concept ($$y$$)", $$y =: x$$ is more like "Thus we arrive at the following concept ($$y$$), which I'll call $$x$$". But it's a matter of personal taste. Again, if there's already a standard on how things are done, let me know. If not it might be a good idea to think about such a standard. --Florian Brucker 11:35, 29 January 2010 (UTC)