final topology

noun

Given a set X, a family of topological spaces (M#95;i,T#95;i)#95;#123;i#92;inI#125; and a family of functions f#95;i#58;M#95;i#92;toX, the final topology is the finest topology on X such that all f#95;i are continuous.

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Meanings

nounfinal topology (plural final topologies)

plural final topologies

  1. mathematicsGiven a set X, a family of topological spaces (M#95;i,T#95;i)#95;#123;i#92;inI#125; and a family of functions f#95;i#58;M#95;i#92;toX, the final topology is the finest topology on X such that all f#95;i are continuous.
Cite this entry
APA

final topology. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/final%20topology

MLA

“final topology.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/final%20topology. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “final topology,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/final%20topology.

Source: final topology on Wiktionary, CC BY-SA 4.0.