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A **transformation semigroup** is a mathematical structure in the field of abstract algebra and functional analysis that consists of all transformations (functions) from a set to itself, along with an operation that describes how to combine these transformations. More formally, a transformation semigroup can be defined as follows: 1. **Set**: Let \( X \) be a non-empty set.

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  1. Semigroup theory
  2. Fields of abstract algebra
  3. Fields of mathematics
  4. Mathematics
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