Wszystkie pola: density topology - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Artykuł

Skocz do pozycji: 2.

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

Skocz do pozycji: 3.

Tytuł:: Ramsey, Lebesgue, and Marczewski sets and the Baire property
Autorzy:: Reardon, Patrick
Powiązania:: https://bibliotekanauki.pl/articles/1205503.pdf
Data publikacji:: 1996
Wydawca:: Polska Akademia Nauk. Instytut Matematyczny PAN
Tematy:: Ramsey set
Marczewski set
perfect set
measurable set
Baire property
density topology
Ellentuck topology
σ-algebra
Opis:: We investigate the completely Ramsey, Lebesgue, and Marczewski σ-algebras and their relations to the Baire property in the Ellentuck and density topologies. Two theorems concerning the Marczewski σ-algebra (s) are presented.

THEOREM. In the density topology D, (s) coincides with the σ-algebra of Lebesgue measurable sets.

THEOREM. In the Ellentuck topology on $[ω]^ω$, $(s)_0$ is a proper subset of the hereditary ideal associated with (s).

We construct an example in the Ellentuck topology of a set which is first category and measure 0 but which is not $B_r$-measurable. In addition, several theorems concerning perfect sets in the Ellentuck topology are presented. In particular, it is shown that there exist countable perfect sets in the Ellentuck topology.
Źródło:: Fundamenta Mathematicae; 1996, 149, 3; 191-203
0016-2736
Pojawia się w:: Fundamenta Mathematicae
Dostawca treści:: Biblioteka Nauki

Artykuł

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