Complete density topology |
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Authors: | W?adys?aw Wilczyński |
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Institution: | a Faculty of Mathematics and Informatics, University of ?ód?, Banacha 22, 90-238 ?ód?,, Poland b Institute of Mathematics, Technical University of ?ód?,, 90-924 ?ód?,, Poland |
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Abstract: | Using the notion of the complete convergence of a sequence of measurable functions we introduce the notion of a complete density point of a measurable set. Using complete density points we generate a topology on the real line between ordinary and density topology. An ingenious construction of Lekkerkerker enables us to prove that the simple density topology is strictly stronger than the complete topology. |
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