Inverse limits have played a very important role in Continuum Theory. Their definition is technical and very precise. Consequently, their general properties are relatively easy to prove and, as we can see in this chapter, most of them can be left as exercises. Moreover, inverse limits are appropriate to construct continua with concrete and workable properties. We prove the Anderson-Choquet Theorem. We prove that for a continuum X the following conditions are equivalent: X is chainable, X is an inverse limit of arcs, and X is arc-like.

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Inverse Limits

  • Alejandro Illanes

摘要

Inverse limits have played a very important role in Continuum Theory. Their definition is technical and very precise. Consequently, their general properties are relatively easy to prove and, as we can see in this chapter, most of them can be left as exercises. Moreover, inverse limits are appropriate to construct continua with concrete and workable properties. We prove the Anderson-Choquet Theorem. We prove that for a continuum X the following conditions are equivalent: X is chainable, X is an inverse limit of arcs, and X is arc-like.