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Let us choose the initial value so that < ′ to be able to apply the iterated “shrinking” lemma. In addition we want s ε 0 < 1 {\displaystyle s\varepsilon _{0}<1} to make sure that ε k {\displaystyle \varepsilon _{k}} decreases as we increase k {\displaystyle k} .
In mathematics, in the field of topology, a topological space is said to have the shrinking property [1] or to be a shrinking space if every open cover admits a shrinking. A shrinking of an open cover is another open cover indexed by the same indexing set, with the property that the closure of each open set in the shrinking lies inside the corresponding original open set.
Download as PDF; Printable version ... generalized the pumping lemma to indexed grammars. Conversely, Gilman [10] [11] gives a "shrinking lemma" for indexed languages ...
Download as PDF; Printable version; ... Hayashi [14] generalized the pumping lemma to indexed ... Gilman [7] gives a "shrinking lemma" for indexed languages. See also ...
Burnside's lemma also known as the Cauchy–Frobenius lemma; Frattini's lemma (finite groups) Goursat's lemma; Mautner's lemma (representation theory) Ping-pong lemma (geometric group theory) Schreier's subgroup lemma; Schur's lemma (representation theory) Zassenhaus lemma
Lemma 2: If is a locally finite open cover, then there are continuous functions : [,] such that and such that := is a continuous function which is always non-zero and finite. Theorem: In a paracompact Hausdorff space X {\displaystyle X\,} , if O {\displaystyle {\mathcal {O}}\,} is an open cover, then there exists a partition of unity ...