disjoint union topology

From Wiktionary, the free dictionary
Jump to navigation Jump to search

English

[edit]

Noun

[edit]

disjoint union topology (plural disjoint union topologies)

  1. (topology) A topology which is applicable to the disjoint union of a given set of topological spaces and is the largest (most inclusive) topology that preserves the continuity of each contributing space as represented in the union.
    • 1978, Maria Louise Shea Terrell, Topological 2-categories and Principal Topological Categories, University of Virginia, page 19:
      The reader will recall that the morphism and object sets of were not necessarily given the disjoint union topologies.
    • 2003, John M. Lee, Introduction to Smooth Manifolds, Springer, page 548:
      Given any indexed collection of topological spaces , we define the disjoint union topology on by declaring a subset of to be open if and only if its intersection with each is open in .
    • 2005, Friedrich Ischebeck, Ravi A. Rao, Ideals and Reality: Projective Modules and Number of Generators of Ideals, Springer, page 118:
      And the set of all sub vector spaces of , i.e. the disjoint union of the , gets the disjoint union topology.

Translations

[edit]

Further reading

[edit]