Definition talk:Everywhere Dense/Real Numbers

There needs to be a page demonstrating that the demonstration of e.d. for real numbers is equivalent to the definition from the point of view of a general topological space. --prime mover (talk) 18:05, 1 February 2017 (EST)

Yes, perhaps. There are many cases like this, where something is defined for common cases separately and then in general. --barto (talk) 01:22, 2 February 2017 (EST)

More than "perhaps" -- they all should. There is an exercise under way (it is unwieldy, due to the nature of the task) to demonstrate that all such definitions that have a "real numbers", a "metric spaces" and a "topology" context, can all be seen to be equivalent. This reflects the history of the development of topology. Then it will be possible to prove certain results in real analysis by means of an argument based entirely on topological arguments.

Hence I am wary of an avalanche of "topological" definitions for objects in the real number domain which use a different definition from the definition in the language of topology without a demonstration for each one showing equivalence. --prime mover (talk) 02:09, 2 February 2017 (EST)