Abstract
We present a density-type topology on the plane generated by the strict convergence of double sequences. The point of restricted density of a measurable set A⊂ℝ×ℝ is defined using a convergence in a restricted sense of a sequence of a form
The definition of a strict density point is a natural modification of the previous notion. We describe operators and topologies generated by them.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Filipczak, M., Wilczyński, W. Strict density topology on the plane. Measure case. Rend. Circ. Mat. Palermo 60, 113–124 (2011). https://doi.org/10.1007/s12215-011-0034-6
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DOI: https://doi.org/10.1007/s12215-011-0034-6