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2010 | 18 | 3 | 175-183
Tytuł artykułu

On the Continuity of Some Functions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We prove that basic arithmetic operations preserve continuity of functions.
Słowa kluczowe
Wydawca
Rocznik
Tom
18
Numer
3
Strony
175-183
Opis fizyczny
Daty
wydano
2010-01-01
online
2011-01-05
Twórcy
  • Institute of Informatics, University of Białystok, Sosnowa 64, 15-887 Białystok, Poland
Bibliografia
  • [1] Grzegorz Bancerek. Cardinal numbers. Formalized Mathematics, 1(2):377-382, 1990.
  • [2] Grzegorz Bancerek. The fundamental properties of natural numbers. Formalized Mathematics, 1(1):41-46, 1990.
  • [3] Grzegorz Bancerek. The ordinal numbers. Formalized Mathematics, 1(1):91-96, 1990.
  • [4] Grzegorz Bancerek and Krzysztof Hryniewiecki. Segments of natural numbers and finite sequences. Formalized Mathematics, 1(1):107-114, 1990.
  • [5] Grzegorz Bancerek and Andrzej Trybulec. Miscellaneous facts about functions. Formalized Mathematics, 5(4):485-492, 1996.
  • [6] Czesław Byliński. The complex numbers. Formalized Mathematics, 1(3):507-513, 1990.
  • [7] Czesław Byliński. Finite sequences and tuples of elements of a non-empty sets. Formalized Mathematics, 1(3):529-536, 1990.
  • [8] Czesław Byliński. Functions and their basic properties. Formalized Mathematics, 1(1):55-65, 1990.
  • [9] Czesław Byliński. Functions from a set to a set. Formalized Mathematics, 1(1):153-164, 1990.
  • [10] Czesław Byliński. Partial functions. Formalized Mathematics, 1(2):357-367, 1990.
  • [11] Czesław Byliński. Some basic properties of sets. Formalized Mathematics, 1(1):47-53, 1990.
  • [12] Czesław Byliński. The sum and product of finite sequences of real numbers. Formalized Mathematics, 1(4):661-668, 1990.
  • [13] Agata Darmochwał. The Euclidean space. Formalized Mathematics, 2(4):599-603, 1991.
  • [14] Agata Darmochwał and Yatsuka Nakamura. Metric spaces as topological spaces - fundamental concepts. Formalized Mathematics, 2(4):605-608, 1991.
  • [15] Artur Korniłowicz. Arithmetic operations on functions from sets into functional sets. Formalized Mathematics, 17(1):43-60, 2009, doi:10.2478/v10037-009-0005-y.[Crossref]
  • [16] Artur Korniłowicz and Yasunari Shidama. Intersections of intervals and balls in ϵn/T. Formalized Mathematics, 12(3):301-306, 2004.
  • [17] Artur Korniłowicz and Yasunari Shidama. Some properties of circles on the plane. Formalized Mathematics, 13(1):117-124, 2005.
  • [18] Beata Padlewska and Agata Darmochwał. Topological spaces and continuous functions. Formalized Mathematics, 1(1):223-230, 1990.
  • [19] Andrzej Trybulec. Binary operations applied to functions. Formalized Mathematics, 1(2):329-334, 1990.
  • [20] Andrzej Trybulec. A Borsuk theorem on homotopy types. Formalized Mathematics, 2(4):535-545, 1991.
  • [21] Andrzej Trybulec. On the sets inhabited by numbers. Formalized Mathematics, 11(4):341-347, 2003.
  • [22] Andrzej Trybulec and Czesław Byliński. Some properties of real numbers. Formalized Mathematics, 1(3):445-449, 1990.
  • [23] Wojciech A. Trybulec. Vectors in real linear space. Formalized Mathematics, 1(2):291-296, 1990.
  • [24] Zinaida Trybulec. Properties of subsets. Formalized Mathematics, 1(1):67-71, 1990.
  • [25] Edmund Woronowicz. Relations and their basic properties. Formalized Mathematics, 1(1):73-83, 1990.
  • [26] Edmund Woronowicz. Relations defined on sets. Formalized Mathematics, 1(1):181-186, 1990.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_v10037-010-0020-z
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