- Tytuł:
- Category theorems concerning Z-density continuous functions
- Autorzy:
-
Ciesielski, K.
Larson, L. - Powiązania:
- https://bibliotekanauki.pl/articles/1215085.pdf
- Data publikacji:
- 1991
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
ℑ-density topology
ℑ-density continuous functions
first category sets - Opis:
- 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.
- Źródło:
-
Fundamenta Mathematicae; 1991-1992, 140, 1; 79-85
0016-2736 - Pojawia się w:
- Fundamenta Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł