Metric Space - Notions of Metric Space Equivalence

Notions of Metric Space Equivalence

Given two metric spaces (M1, d1) and (M2, d2):

  • They are called homeomorphic (topologically isomorphic) if there exists a homeomorphism between them (i.e., a bijection continuous in both directions).
  • They are called uniformic (uniformly isomorphic) if there exists a uniform isomorphism between them (i.e., a bijection uniformly continuous in both directions).
  • They are called isometric if there exists a bijective isometry between them. In this case, the two metric spaces are essentially identical.
  • They are called quasi-isometric if there exists a quasi-isometry between them.

Read more about this topic:  Metric Space

Famous quotes containing the words notions of, notions and/or space:

    “Assumptions that racism is more oppressive to black men than black women, then and now ... based on acceptance of patriarchal notions of masculinity.”
    —bell hooks (b. c. 1955)

    “The mass believes that it has the right to impose and to give force of law to notions born in the café.”
    —José Ortega Y Gasset (1883–1955)

    “In the tale proper—where there is no space for development of character or for great profusion and variety of incident—mere construction is, of course, far more imperatively demanded than in the novel.”
    —Edgar Allan Poe (1809–1849)