Inverse limits with irreducible set-valued functions
نویسندگان
چکیده
منابع مشابه
Tree-likeness of Certain Inverse Limits with Set-valued Functions
Inverse limits with set-valued functions having graphs that are the union of mappings have attracted some attention over the past few years. In this paper we show that if the graph of a surjective set-valued function f : [0, 1] → 2[0,1] is the union of two mappings having only one point (x, x) in common such that x is not the image of any other point of the interval under f , then its inverse l...
متن کاملSome Structure Theorems for Inverse Limits with Set-valued Functions
We investigate inverse limits with set-valued bonding functions. We generalize theorems of W. T. Ingram and William S. Mahavier, and of Van Nall, on the connectedness of the inverse limit space. We establish a fixed point theorem and show that under certain conditions, inverse limits with set-valued bonding functions can be realized as ordinary inverse limits. We also obtain some results that a...
متن کاملOne-dimensional Inverse Limits with Set-valued Functions
In this paper we show that an inverse limit is 1-dimensional whenever the bonding functions are upper semi-continuous from [0, 1] into C([0, 1]) and dim(G(fi ◦ fi+1 ◦ · · · ◦ fj)) = 1 for all integers i and j, 1 ≤ i ≤ j. We apply this result to show that such an inverse limit is treelike and also to show that unions of certain finite collections of interval-valued upper semi-continuous function...
متن کاملInverse Limits of Families of Set-valued Functions
In this paper we investigate inverse limits of two related parameterized families of upper semi-continuous set-valued functions. We include a theorem one consequence of which is that certain inverse limits with a single bonding function from one of these families are the closure of a topological ray (usually with indecomposable remainder). Also included is a theorem giving a new sufficient cond...
متن کاملInverse Limits of Upper Semi-continuous Set Valued Functions
In this article we define the inverse limit of an inverse sequence (X1, f1), (X2, f2), (X3, f3), . . . where each Xi is a compact Hausdorff space and each fi is an upper semi-continuous function from Xi+1 into 2i . Conditions are given under which the inverse limit is a Hausdorff continuum and examples are given to illustrate the nature of these inverse limits.
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: Topology and its Applications
سال: 2014
ISSN: 0166-8641
DOI: 10.1016/j.topol.2014.02.001