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Simple density topology. (English) Zbl 1194.26002

Summary: We introduce a new topology on the real line generated by the simple density points for measure. We show also that a simple category density point does not lead to a new notion.

MSC:

26A12 Rate of growth of functions, orders of infinity, slowly varying functions
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References:

[1] Bruckner, A.M;Differentiation of Real Functions, Lecture Notes in Mathematics 659, Springer Verlag, 1978. · Zbl 0382.26002
[2] Ciesielski K, Larso, L, Ostaszewski K,I-density continuous functions, Memoirs A.M.S.,515, 1994. · Zbl 0801.26001
[3] Goffman, C.; Neugebauer, C. J.; Nishiura, T., The density topology and approximate continuity, Duke Math. J., 28, 497-506 (1961) · Zbl 0101.15502
[4] Oxtoby J. C,Measure and Category, Springer Verlag 1981.
[5] Poreda, W.; Wagner-Bojakowska, E.; Wilczynski, W., A category analogue of the density topology, Fund. Math., 125, 167-173 (1985) · Zbl 0613.26002
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