disjoint union topology

plural disjoint union topologies

1. mathematicsA 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.

   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

   2 more examples

   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

   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