initial 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;X#92;toM#95;i, the initial topology is the coarsest topology on X such that all f#95;i are continuous.

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Meanings

nouninitial topology (plural initial topologies)

plural initial 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;X#92;toM#95;i, the initial topology is the coarsest topology on X such that all f#95;i are continuous.
Cite this entry
APA

initial topology. (n.d.). In WatkinsX Dictionary. Retrieved November 2, 2026, from https://dictionary.watkinsx.com/word/initial%20topology

MLA

“initial topology.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/initial%20topology. Accessed November 2, 2026.

Chicago

WatkinsX Dictionary, s.v. “initial topology,” accessed November 2, 2026, https://dictionary.watkinsx.com/word/initial%20topology.

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