Last Updated
：2025/12/06
initial topology
Noun
Japanese Meaning
与えられた集合 X と、各々の位相空間 (M_i, T_i) と写像 f_i: X → M_i の族に対して、すべての f_i が連続となるような、X 上の位相の中で最も粗い位相。
（ plural ）
Quizzes for review
(topology) Given a set X, a family of topological spaces (M_i,T_i)_(i∈I) and a family of functions f_i:X→M_i, the initial topology is the coarsest topology on X such that all f_i are continuous.
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initial topology
To ensure each map f_i:X→M_i is continuous, we endow X with the initial topology induced by the family of functions f_i.
See correct answer
To ensure each map f_i:X→M_i is continuous, we endow X with the initial topology induced by the family of functions f_i.
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