Separating sets by Darboux-like functions
نویسندگان
چکیده
منابع مشابه
Some Additive Darboux–like Functions
In this note we will construct several additive Darboux-like functions f : R → R answering some problems from (an earlier version of) [4]. In particular, in Section 2 we will construct, under different additional set theoretical assumptions, additive almost continuous (in sense of Stallings) functions f : R → R whose graph is either meager or null in the plane. In Section 3 we will construct an...
متن کاملLineability, Spaceability, and Additivity Cardinals for Darboux-like Functions
We introduce the concept of maximal lineability cardinal number, mL(M), of a subset M of a topological vector space and study its relation to the cardinal numbers known as: additivity A(M), homogeneous lineability HL(M), and lineability L(M) of M . In particular, we will describe, in terms of L, the lineability and spaceability of the families of the following Darboux-like functions on Rn, n ≥ ...
متن کاملSeparating bichromatic point sets by L-shapes
Given a set R of red points and a set B of blue points in the plane, we study the problem of determining all angles for which there exists an L-shape containing all points from B and no points from R. We propose a worst-case optimal algorithm to solve this problem in O(n) time and O(n) storage, where n = |R| + |B|. We also describe an output-sensitive algorithm that reports these angles in O(n ...
متن کاملMinimal Separating Sets for
For a Muller automaton only a subset of its states is needed to decide whether a run is accepting or not: The set I the innnitely often visited states can be replaced by the intersection I \ W with a xed set W of states, provided W is large enough to distinguish between accepting and non-accepting loops in the automaton. We call such a subset W a separating set. Whereas the idea was previously ...
متن کاملThin classes of separating sets
There are various definitions for a Martin–Pour-El theory in the literature. We isolate two such definitions: weak Martin–Pour-El theories (which correspond to perfect thin Π1 classes) and strong Martin–Pour-El theories (which correspond to thin classes of separating sets). By concentrating on constructions of appropriate Π1 classes, rather than on direct constructions of the theories, we show ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2002
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm175-3-4