topological vector space

noun

A vector space over a topological field endowed with a topology (often the real or complex numbers with standard topology) such that vector addition and scalar multiplication are continuous functions.

Similar
linear topological space
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Meanings

nountopological vector space (plural topological vector spaces)

plural topological vector spaces

  1. functional analysisA vector space over a topological field endowed with a topology (often the real or complex numbers with standard topology) such that vector addition and scalar multiplication are continuous functions.

    Synonyms: linear topological space

Synonyms & antonyms

nounA vector space over a topological field endowed with a topology (often the real or complex numbers with standard topology) such that vector addition and scalar multiplication are continuous functions.

Similar
linear topological space

Translations

Bulgarian линейно топологично пространство
  • линейно топологично пространство (linejno topologično prostranstvo)vector space over a topological field
Cite this entry
APA

topological vector space. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/topological%20vector%20space

MLA

“topological vector space.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/topological%20vector%20space. Accessed November 4, 2026.

Chicago

WatkinsX Dictionary, s.v. “topological vector space,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/topological%20vector%20space.

Source: topological vector space on Wiktionary, CC BY-SA 4.0.