Negligible Sets for Real Connectivity Functions
نویسندگان
چکیده
منابع مشابه
Negligible sets in Erdős spaces
Both spaces were introduced and shown to be one-dimensional but totally disconnected by Paul Erdős [9] in 1940. This result together with the obvious fact that E and Ec are homeomorphic to their squares make these spaces important examples in Dimension Theory. Both E and Ec are universal spaces for the class of almost zero-dimensional spaces; see [7, Theorem 4.15]. A subset of a space is called...
متن کاملNegligible Sets of Radon Measures
Let m be a Radon measure on a Hausdorff topological space X. Corresponding to three kinds of outer measures, three kinds of m-negligible sets are considered. The main theorem states that in a metacompact space X each locally m-negligible set is m-negligible. For a Radon measure in a HausdorfT topological space X we distinguish three kinds of negligible sets corresponding to three kinds of outer...
متن کاملConnectivity properties of Julia sets of Weierstrass elliptic functions
We discuss the connectivity properties of Julia sets of Weierstrass elliptic ℘ functions, accompanied by examples. We give sufficient conditions under which the Julia set is connected and show that triangular lattices satisfy this condition. We also give conditions under which the Fatou set of ℘ contains a toral band and provide an example of an order two elliptic function on a square lattice w...
متن کاملEffectively closed sets and graphs of computable real functions
In this paper, we compare the computability and complexity of a continuous real function F with the computability and complexity of the graph G of the function F . A similar analysis will be carried out for functions on subspaces of the real line such as the Cantor space, the Baire space and the unit interval. In particular, we de1ne four basic types of e"ectively closed sets C depending on whe...
متن کاملThe Kurzweil Integral with Exclusion of Negligible Sets
We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of δ-fine partitions by excluding small sets.
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: Proceedings of the American Mathematical Society
سال: 1970
ISSN: 0002-9939
DOI: 10.2307/2036344