Last Updated
：2025/11/21
topological space
Noun
formal
broadly
Japanese Meaning
位相空間：集合 X と、その上で定められる位相 τ（X の部分集合の集まりで、特定の公理―例えば、X と空集合を含み、任意の合併及び有限個の交わりが位相に含まれる―を満たす）が定める順序対のこと。
Sense（1）
（ plural ）
Quizzes for review
(topology, formally) An ordered pair (X, τ), where X is a set and τ, called the topology, is a collection of subsets of X which satisfies certain axioms and whose elements are called the open sets (or alternatively, for a different set of axioms, the closed sets);
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topological space
To prove that a function is continuous, it suffices to show that the preimage of every open set in the codomain is open in the topological space.
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To prove that a function is continuous, it suffices to show that the preimage of every open set in the codomain is open in the topological space.
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