Geodesic
Category theorems concerning $\mathcal I$-density continuous functions
Krzysztof Ciesielski1 ; Lee Larson2
1 Department of Mathematics West Virginia University Morgantown, West Virginia 26506 U.S.A.
2 Department of Mathematics University of Louisville Louisville, Kentucky 40292 U.S.A
Fundamenta Mathematicae, Tome 140 (1991) no. 1, pp. 79-85.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

The ℑ-density topology $T_ℑ$ on ℝ is a refinement of the natural topology. It is a category analogue of the density topology [9, 10]. This paper is concerned with ℑ-density continuous functions, i.e., the real functions that are continuous when the ℑ-density} topology is used on the domain and the range. It is shown that the family $C_ℑ$ of ordinary continuous functions f: [0,1]→ℝ which have at least one point of ℑ-density continuity is a first category subset of C([0,1])= {f: [0,1]→ℝ: f is continuous} equipped with the uniform norm. It is also proved that the class $C_ℑℑ$ of ℑ-density continuous functions, equipped with the topology of uniform convergence, is of first category in itself. These results remain true when the ℑ-density topology is replaced by the deep ℑ-density topology.
DOI : 10.4064/fm_1991_140_1_1_79_85
Keywords: ℑ-density topology, ℑ-density continuous functions, first category sets

Krzysztof Ciesielski 1 ; Lee Larson 2

1 Department of Mathematics West Virginia University Morgantown, West Virginia 26506 U.S.A.
2 Department of Mathematics University of Louisville Louisville, Kentucky 40292 U.S.A 
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Krzysztof Ciesielski; Lee Larson. Category theorems concerning $\mathcal I$-density continuous functions. Fundamenta Mathematicae, Tome 140 (1991) no. 1, pp. 79-85. doi : 10.4064/fm_1991_140_1_1_79_85. http://geodesic.mathdoc.fr/articles/10.4064/fm_1991_140_1_1_79_85/

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