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The Density Topology On The Reals With Analogues On Other Spaces, Stuart Nygard
The Density Topology On The Reals With Analogues On Other Spaces, Stuart Nygard
Boise State University Theses and Dissertations
A point x is a density point of a set A if all of the points except a measure zero set near to x are contained in A. In the usual topology on ℝ, a set is open if shrinking intervals around each point are eventually contained in the set. The density topology relaxes this requirement. A set is open in the density topology if for each point, the limit of the measure of A contained in shirking intervals to the measure of the shrinking intervals themselves is one. That is, for any point x and a small enough …