PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2006 | 14 | 4 | 213-219
Tytuł artykułu

Baire's Category Theorem and Some Spaces Generated from Real Normed Space1

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
As application of complete metric space, we proved a Baire's category theorem. Then we defined some spaces generated from real normed space and discussed each of them. In the second section, we showed the equivalence of convergence and the continuity of a function. In other sections, we showed some topological properties of two spaces, which are topological space and linear topological space generated from real normed space.
Słowa kluczowe
Wydawca
Rocznik
Tom
14
Numer
4
Strony
213-219
Opis fizyczny
Daty
wydano
2006-01-01
online
2008-06-13
Twórcy
autor
  • Gifu National College of Technology, Gifu, Japan
  • Shinshu University, Nagano, Japan
  • Shinshu University, Nagano, Japan
Bibliografia
  • [1] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [2] Grzegorz Bancerek. The "way-below" relation. Formalized Mathematics, 6(1):169-176, 1997.
  • [3] Leszek Borys. Paracompact and metrizable spaces. Formalized Mathematics, 2(4):481-485, 1991.
  • [4] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [5] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [6] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [7] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [8] Czesław Byliński. Introduction to real linear topological spaces. Formalized Mathematics, 13(1):99-107, 2005.
  • [9] Agata Darmochwał. Compact spaces. Formalized Mathematics, 1(2):383-386, 1990.
  • [10] Alicia de la Cruz. Totally bounded metric spaces. Formalized Mathematics, 2(4):559-562, 1991.
  • [11] Stanisława Kanas and Adam Lecko. Sequences in metric spaces. Formalized Mathematics, 2(5):657-661, 1991.
  • [12] Stanisława Kanas and Adam Lecko, and Mariusz Startek. Metric spaces. Formalized Mathematics, 1(3):607-610, 1990.
  • [13] Zbigniew Karno. Continuity of mappings over the union of subspaces. Formalized Mathematics, 3(1):1-16, 1992.
  • [14] Takaya Nishiyama, Keiji Ohkubo, and Yasunari Shidama. The continuous functions on normed linear spaces. Formalized Mathematics, 12(3):269-275, 2004.
  • [15] Beata Padlewska. Families of sets. Formalized Mathematics, 1(1):147-152, 1990.
  • [16] Beata Padlewska. Locally connected spaces. Formalized Mathematics, 2(1):93-96, 1991.
  • [17] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • [18] Jan Popiołek. Real normed space. Formalized Mathematics, 2(1):111-115, 1991.
  • [19] Bartłomiej Skorulski. First-countable, sequential, and Frechet spaces. Formalized Mathematics, 7(1):81-86, 1998.
  • [20] Bartłomiej Skorulski. The sequential closure operator in sequential and Frechet spaces. Formalized Mathematics, 8(1):47-54, 1999.
  • [21] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
  • [22] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
  • [23] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
  • [24] Andrzej Trybulec. Baire spaces, Sober spaces. Formalized Mathematics, 6(2):289-294, 1997.
  • [25] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [26] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [27] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-006-0024-x
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.