Join Our Newsletter

Free Online Productivity Tools
i2Speak
i2Symbol
i2OCR
iTex2Img
iWeb2Print
iWeb2Shot
i2Type
iPdf2Split
iPdf2Merge
i2Bopomofo
i2Arabic
i2Style
i2Image
i2PDF
iLatex2Rtf
Sci2ools

JUCS

2010

2010

: We investigate the relationship between computable metric spaces (X, d, ) and (X, d, ), where (X, d) is a given metric space. In the case of Euclidean space, and are equivalent up to isometry, which does not hold in general. We introduce the notion of effectively dispersed metric space and we use it in the proof of the following result: if (X, d, ) is effectively totally bounded, then (X, d, ) is also effectively totally bounded. This means that the property that a computable metric space is effectively totally bounded (and in particular effectively compact) depends only on the underlying metric space. In the final section of this paper we examine compact metric spaces (X, d) such that there are only finitely many isometries X X. We prove that in this case a stronger result holds than the previous one: if (X, d, ) is effectively totally bounded, then and are equivalent. Hence if (X, d, ) is effectively totally bounded, then (X, d) has a unique computability structure. Key Words: ...

Related Content

Added |
20 May 2011 |

Updated |
20 May 2011 |

Type |
Journal |

Year |
2010 |

Where |
JUCS |

Authors |
Zvonko Iljazovic |

Comments (0)