Definition talk:Continuous Mapping (Topology)/Everywhere

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I see the introduction of "continuous everywhere mapping". Is this even English? "Everywhere continuous mapping" sounds much better.

But why are we not sticking with "continuous mapping" to begin with? I'm afraid this choice is going to lead to confusion because we're deviating from practically all of the literature. What is the motivation behind this choice? — Lord_Farin (talk) 05:50, 14 January 2018 (EST)

Trying to distinguish between a mapping which is continuous only on a subset of a topological space, and one which is continuous everywhere on that space. The link Definition:Continuous Mapping (Topology) is the overall page which subsumes all gradations. I am trying to get the site to fit in with the evolving philosophy that every refinement of a concept must be linked to precisely. I gather there is still some evolution to happen before we arrive at the crown of creation. --prime mover (talk) 05:59, 14 January 2018 (EST)
I note your point about "continuous everywhere mapping" and I will start to use the already-in-place "everywhere continuous mapping" instead -- although the verbose alternative proposed and implemented by Barto I'm not so sure about. --prime mover (talk) 06:19, 14 January 2018 (EST)