Continuity of all Algorithmic Functions on Left Numbers

Research Article
Open access

Continuity of all Algorithmic Functions on Left Numbers

Weixi Chen 1* , Wenkuan Zhang 2
  • 1 Nanjing Foreign Language School, Nanjing 210036, China    
  • 2 Kunlun, RDFZ Chaoyang Branch School, Beijing 100028, China    
  • *corresponding author ch.weixi@outlook.com
TNS Vol.5
ISSN (Print): 2753-8826
ISSN (Online): 2753-8818
ISBN (Print): 978-1-915371-53-9
ISBN (Online): 978-1-915371-54-6

Abstract

A constructive Function is a computer program that transforms a Constructive Real Number (CRN) into another CRN. A left number is a program that generates an increasing sequence of rational numbers with an upper bound. We use algorithmic functions to generate CRNs and Left numbers. In this essay, we will prove the continuity of such functions on Left numbers in topological space with the base of right rays.

Keywords:

CF (constructive function), algorithmic functions, CRN (constructive real number), Left number, Topological space

Chen,W.;Zhang,W. (2023). Continuity of all Algorithmic Functions on Left Numbers. Theoretical and Natural Science,5,47-52.
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References

[1]. Munkres, J. R. (2000). Topology (Vol. 2). Upper Saddle River: Prentice Hall.

[2]. BrunkChavez, Beth L . Co-author with Nancy V. Wood. Instructor's Manual for College Reading. Up-per Saddle River : Prentice Hall,[J]. 2013.

[3]. E. Bishop (2012) “Foundations of Constructive Analysis”. Ishi Press

[4]. Robinson A . Reviews: Foundations of Constructive Analysis.[J]. Amer.math.monthly, 1968(8):920-921.

[5]. B. A. Kushner (1984) “Lectures on Constructive Mathematical Analysis”. Translated by E. Mendelson. American Mathematical Society

[6]. VOLKERMICHEL. LECTURES ON CONSTRUCTIVE APPROXIMATION[M].

[7]. Shen and N. K. Vereshchagin (2002) “Computable Functions”. Translated by V. N. Dubrovskii. American Mathematical Society

[8]. Turing (1937) “On Computable Numbers, with an Application to the Entscheidungsproblem” Pro-ceeding of the London Mathematical Society, Vol S2-42, Issue 1, pages 230-265

[9]. Goto S . A.M.Turing: On Computable Numbers, with an Application to the Entscheidungsproblem[J]. IPSJ Magazine, 2002, 43.

Cite this article

Chen,W.;Zhang,W. (2023). Continuity of all Algorithmic Functions on Left Numbers. Theoretical and Natural Science,5,47-52.

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The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.

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About volume

Volume title: Proceedings of the 2nd International Conference on Computing Innovation and Applied Physics (CONF-CIAP 2023)

ISBN：978-1-915371-53-9(Print) / 978-1-915371-54-6(Online)
Editor：Marwan Omar, Roman Bauer
Conference website: https://www.confciap.org/
Conference date: 25 March 2023
Series: Theoretical and Natural Science
Volume number: Vol.5
ISSN：2753-8818(Print) / 2753-8826(Online)

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References

[1]. Munkres, J. R. (2000). Topology (Vol. 2). Upper Saddle River: Prentice Hall.

[2]. BrunkChavez, Beth L . Co-author with Nancy V. Wood. Instructor's Manual for College Reading. Up-per Saddle River : Prentice Hall,[J]. 2013.

[3]. E. Bishop (2012) “Foundations of Constructive Analysis”. Ishi Press

[4]. Robinson A . Reviews: Foundations of Constructive Analysis.[J]. Amer.math.monthly, 1968(8):920-921.

[5]. B. A. Kushner (1984) “Lectures on Constructive Mathematical Analysis”. Translated by E. Mendelson. American Mathematical Society

[6]. VOLKERMICHEL. LECTURES ON CONSTRUCTIVE APPROXIMATION[M].

[7]. Shen and N. K. Vereshchagin (2002) “Computable Functions”. Translated by V. N. Dubrovskii. American Mathematical Society

[8]. Turing (1937) “On Computable Numbers, with an Application to the Entscheidungsproblem” Pro-ceeding of the London Mathematical Society, Vol S2-42, Issue 1, pages 230-265

[9]. Goto S . A.M.Turing: On Computable Numbers, with an Application to the Entscheidungsproblem[J]. IPSJ Magazine, 2002, 43.

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