Recently I have heard about the so-called fiber space？And it is said that it is a kind of generalization of fiber bundle.So what is fiber space？How dose it relate to the fiber bundle？Thanks！
2026-03-26 18:50:46.1774551046
What is fiber space？Is it related to the fiber bundle？
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Yes, it really depends on the the context. A fibre space is sometimes referred to as a fibre bundle or a fibration.
Consider an object $(X,π,B),$ where $π:X→B$ is a continuous surjective mapping of a topological space $X$ onto a topological space $B$ (i.e., a fibration).
A fibre space can be regarded as the union of the fibres $π←[{b}],$ parametrized by the base space $B$ and glued by the topology of $X.$