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Difference (from prior minor revision) (major diff, author diff)

Changed: 6c6
the inverse limit, A, as the set of all mappings
the inverse limit, A, as the set of all mappings

Changed: 8c8
lattice to the union of all Aj such that for every i
lattice to the union of all Aj such that for every i

Changed: 12c12
The inverse limit together with the functions
The inverse limit A together with the functions

Changed: 17c17
gj = gi o fi,j'' there is a unique
gj = gi o fi,j there is a unique

Changed: 19c19
gi = g o fi
gi = g o fi.

Changed: 21,23c21,23
Note that A is often the same kind of algebraic structure with the
operations defined element-wise: this holds for rings, algebras, fields,
groups and vector spaces, amongst other. If every structure is finite,
Note that A is often the same kind of algebraic structure as the Ai, with the
operations defined element-wise: this holds for rings, algebras, fields,
groups and vector spaces, amongst other. If every structure is finite,

Changed: 28c28
Examples:
Examples:

Changed: 30c30
* Zp, the p-adic numbers are an inverse limit of Z/pn with the lattice being the natural numbers with the usual order, and the functions being "take reminder". The natural topology on the p-adic numbers is the same as the one described here.
* Zp, the p-adic integers, are the inverse limit of Z/pn (see modular arithmetic) with the lattice being the natural numbers with the usual order, and the functions being "take remainder". The natural topology on the p-adic integers is the same as the one described here.
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Last edited December 8, 2001 7:06 am by Derek Ross (diff)
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