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Glite Dictionary
pseudometric space

pseudometric space

9.9
A space where different points can have distance zero
  • noun
  • /ˈsuːdəˌmɛtrɪk speɪs/
  • Specialized
translation icon : espacio pseudométrico
  • In a pseudometric space, two distinct points can have a distance of zero.

Examples

  • Unlike a metric space, a pseudometric space does not require the distance function to separate all points.

  • A pseudometric space allows two different points to have a distance of zero.

  • In functional analysis, examples of a pseudometric space commonly arise when studying seminorms.

  • Many mathematicians study pseudometric spaces for their unique properties.

  • A pseudometric space allows for the possibility that the distance between two distinct points can be zero.

  • In a pseudometric space, it is possible for two different points to have a distance of zero between them.

  • Many theorems in topology are developed based on the properties of a pseudometric space.

Synonyms

semi-metric space
vspseudometric space
  • Specialized
9.9

A set of points where two different points can have zero distance

is the same concept but uses an alternative technical name

Surface Forms

pseudometric space singular
pseudometric spaces plural

Morphology

pseudometric + space

The noun phrase is directly compositional: 'pseudometric' describes the type of 'space', so the meaning is simply 'a space that is equipped with a pseudometric'. Even though 'pseudometric' is a technical term, if a learner knows the constituent words (or the morphemes pseudo- + metric) they can infer the MWE as a space characterised by that measurement function.

Etymology

Pseudometric space comes from the parts pseudo (meaning 'not real' or 'seeming') and metric (a way to measure 'distance'). Imagine a ruler that sometimes says two different points are 'zero' apart, like two people who share the same house number—the ruler treats them as the same place even though they are different. So the name helps remember that this space measures distance but can give 'zero' distance to different points.