Dictionary

disjoint union topology en · NOUN

Meanings

1. 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.
   • Given any indexed collection of topological spaces #92;left#92;#123;X#95;#92;alpha#92;right#92;#125;#95;#123;#92;alpha#92;inA#125;, we define the disjoint union topology on #92;textstyle#92;coprod#95;#123;#92;alpha#92;inA#125;X#95;#92;alpha by declaring a subset of #92;textstyle#92;coprod#95;#123;#92;alpha#92;inA#125;X#95;#92;alpha to be open if and only if its intersection with each X#95;#92;alpha is open in X#95;#92;alpha. 2003, John M. Lee, Introduction to Smooth Manifolds, Springer, page 548:
   • The reader will recall that the morphism and object sets of A'#61;#92;coprod#95;#123;p,q#92;inP#125;A#95;c(q,p) were not necessarily given the disjoint union topologies. 1978, Maria Louise Shea Terrell, Topological 2-categories and Principal Topological Categories, University of Virginia, page 19:
   • And the set Gⁿ(#92;mathbb#123;F#125;) of all sub vector spaces of #92;mathbb#123;F#125;ⁿ, i.e. the disjoint union of the Gⁿ#95;k(#92;mathbb#123;F#125;), gets the disjoint union topology. 2005, Friedrich Ischebeck, Ravi A. Rao, Ideals and Reality: Projective Modules and Number of Generators of Ideals, Springer, page 118:

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