Word.ws English Dictionary

sober space

sober space noun: a topological space of which every join-irreducible closed subset is the closure of exactly one point of the space.

Noun

sober space (plural sober spaces)

  1. A topological space of which every join-irreducible closed subset is the closure of exactly one point of the space.
    • For a reader more interested in function spaces than in functors, this concludes the description of content except to add that the classification of coadjoint G’s by sets B bearing a topological topology relativizes to T₀ spaces. For other readers: and trivially to sober spaces.1975, Mathematica Scandinavica, Societates Mathematicae, page 318
    • In the Hofmann and Lawson paper, it is proved that the topological space Spec(L) is a locally quasicompact sober space […] .1983, Houston Journal of Mathematics, Volume 9, University of Houston, page 192

Examples of sober space in a sentence

  • How rich are sober and L-sober spaces, are there important examples?2003, A. Pultr, S. E. Rodabaugh, “Chapter 6: Lattice-Valued Frames, Functor Categories, And Classes of Sober Spaces”, in Stephen Ernest...
  • When X is a noetherian sober space the construction of loc. cit. can be extended to an arbitrary lower-semicontinuous function for the constructible topology.2004, Ofer Gabber, “Notes on some t-structures”, in Alan Adolphson, Francesco Baldassarri, Pierre Berthelot, Nicholas Katz, François...

Forms of sober space

pluralsober spaces

Questions about sober space

What does sober space mean?
Sober space means a topological space of which every join-irreducible closed subset is the closure of exactly one point of the space.
How do you use sober space in a sentence?
How rich are sober and L-sober spaces, are there important examples?
What part of speech is sober space?
Sober space is a noun.
What is the plural of sober space?
The plural of sober space is sober spaces.

Words near sober space in the dictionary

  1. sober down
  2. sober house
  3. sober lite
  4. sober living house
  5. sober living houses
  6. sober space
  7. sober spaces
  8. sober up
  9. sober-curious
  10. Soberano
  11. Soberanos

Source and license

Adapted from Wiktionary: sober space (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “sober space.” Word.ws, https://word.ws/sober_space. Based on Wiktionary, CC BY-SA 4.0.