Category:Definitions/Towers

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This category contains definitions related to Towers.
Related results can be found in Category:Towers.


Let $X$ be a set.

Let $T$ be any non-empty subset of $X$

Let $c$ be a fixed choice function on the non-empty subsets $T$ of $X$.

Let $\preccurlyeq$ be a well-ordering on $T$.


The well-ordered set $\struct {T, \preccurlyeq}$ is a tower in $X$ if and only if, for all $t \in T$:

$t = \map c {X \setminus \map {S_t} T}$

where $\map {S_t} T$ is the initial segment of $T$ determined by $t$.

Pages in category "Definitions/Towers"

The following 3 pages are in this category, out of 3 total.