 ##  [Loss of Compactness](/loss-compactness) 

  ##  [Loss of Compactness](https://mathlogic.quantumdictionary.io/loss-compactness-0) 

  
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- Natural &amp; Formal Sciences -

**Mathematics &amp; Logic Dictionary**

 
Definition

A failure mode in which a bounded sequence in a function space does not contain a strongly convergent subsequence due to translation, concentration, or oscillation effects; boundedness alone is insufficient to secure precompactness in infinite-dimensional or noncompact domains.