Generating Countable Sets of Surjective Functions
نویسنده
چکیده
We prove that any countable set of surjective functions on an infinite set of cardinality אn with n ∈ N can be generated by at most n/2 + 9n/2 + 7 surjective functions of the same set; and there exist n/2 + 9n/2 + 7 surjective functions that cannot be generated by any smaller number of surjections. We also present several analogous results for other classical infinite transformation semigroups such as the injective functions, the Baer-Levi semigroups, and the Schützenberger monoids.
منابع مشابه
Course 221: Michaelmas Term 2006 Section 1: Sets, Functions and Countability
1 Sets, Functions and Countability 2 1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Cartesian Products of Sets . . . . . . . . . . . . . . . . . . . . 5 1.3 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Equivalence Relations . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Functions . . . . . . . . . . . . . . . . . . . . . . . . ...
متن کاملGenerating Uncountable Transformation Semigroups
We consider naturally occurring, uncountable transformation semigroups S and investigate the following three questions. (i) Is every countable subset F of S also a subset of a finitely generated subsemigroup of S? If so, what is the least number n such that for every countable subset F of S there exist n elements of S that generate a subsemigroup of S containing F as a subset. (ii) Given a subs...
متن کاملSierpiński Index of Classical Transformation Semigroups
We prove that any countable set of surjective functions on an infinite set of cardinality אn with n ∈ N can be generated by at most n2/2 + 9n/2 + 5 surjective functions of the same set; and there exist n2/2 + 9n/2 + 5 surjective functions that cannot be generated by any smaller number of surjections. If injective functions are considered instead of surjective functions, then n + 4 replaces n2/2...
متن کاملCOUNTABLE COMPACTNESS AND THE LINDEL¨OF PROPERTY OF L-FUZZY SETS
In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...
متن کاملThe generation of fuzzy sets and the~construction of~characterizing functions of~fuzzy data
Measurement results contain different kinds of uncertainty. Besides systematic errors andrandom errors individual measurement results are also subject to another type of uncertainty,so-called emph{fuzziness}. It turns out that special fuzzy subsets of the set of real numbers $RR$are useful to model fuzziness of measurement results. These fuzzy subsets $x^*$ are called emph{fuzzy numbers}. The m...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010