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2006 | 14 | 3 | 93-100

Tytuł artykułu

Connectedness and Continuous Sequences in Finite Topological Spaces

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
First, equivalence conditions for connectedness are examined for a finite topological space (originated in [9]). Secondly, definitions of subspace, and components of the subspace of a finite topological space are given. Lastly, concepts of continuous finite sequence and minimum path of finite topological space are proposed.

Słowa kluczowe

Wydawca

Rocznik

Tom

14

Numer

3

Strony

93-100

Opis fizyczny

Daty

wydano
2006-01-01
online
2008-06-09

Twórcy

  • Shinshu University, Nagano, Japan

Bibliografia

  • [1] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [2] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [3] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [4] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [5] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [6] Hiroshi Imura and Masayoshi Eguchi. Finite topological spaces. Formalized Mathematics, 3(2):189-193, 1992.
  • [7] Hiroshi Imura, Masami Tanaka, and Yatsuka Nakamura. Continuous mappings between finite and one-dimensional finite topological spaces. Formalized Mathematics, 12(3):381-384, 2004.
  • [8] Jarosław Kotowicz. Functions and finite sequences of real numbers. Formalized Mathematics, 3(2):275-278, 1992.
  • [9] Yatsuka Nakamura. Finite topology concept for discrete spaces. In H. Umegaki, editor, Proceedings of the Eleventh Symposium on Applied Functional Analysis, pages 111-116, Noda-City, Chiba, Japan, 1988. Science University of Tokyo.
  • [10] Takaya Nishiyama and Yasuho Mizuhara. Binary arithmetics. Formalized Mathematics, 4(1):83-86, 1993.
  • [11] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • [12] Masami Tanaka and Yatsuka Nakamura. Some set series in finite topological spaces. Fundamental concepts for image processing. Formalized Mathematics, 12(2):125-129, 2004.
  • [13] Andrzej Trybulec. Subsets of complex numbers. To appear in Formalized Mathematics.
  • [14] Andrzej Trybulec. Domains and their Cartesian products. Formalized Mathematics, 1(1):115-122, 1990.
  • [15] Andrzej Trybulec. Enumerated sets. Formalized Mathematics, 1(1):25-34, 1990.
  • [16] Andrzej Trybulec. Tarski Grothendieck set theory. Formalized Mathematics, 1(1):9-11, 1990.
  • [17] Wojciech A. Trybulec. Pigeon hole principle. Formalized Mathematics, 1(3):575-579, 1990.
  • [18] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [19] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_2478_v10037-006-0011-2
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