On $r$-separated sets in normed spaces
نویسندگان
چکیده
منابع مشابه
t-proximinal sets in fuzzy normed spaces
The main purpose of this paper, is to investigate the basic properties of t-proximinal sets. At first we prove some main results and then we see some classified cases, in finite dimensional fuzzy normed spaces.
متن کاملIntersections of Centred Sets in Normed Spaces
Various kinds of closed centred sets in normed spaces are considered. Necessary and sufficient conditions are obtained for every decreasing sequence of such sets to have nonempty intersection. Let X be a real or complex normed space. Recall that a set S ⊆ X is symmetric if S = −S and balanced if tS ⊆ S for all t ∈ [−1, 1]. It is convenient to introduce the following definitions. Definitions. 1....
متن کامل$r$-fuzzy regular semi open sets in smooth topological spaces
In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed) sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed) sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure) operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the ...
متن کاملOn the Size of Approximately Convex Sets in Normed Spaces
Let X be a normed space. A set A ⊆ X is approximately convex if d(ta + (1 − t)b, A) ≤ 1 for all a, b ∈ A and t ∈ [0, 1]. We prove that every n-dimensional normed space contains approximately convex sets A with H(A,Co(A)) ≥ log2 n− 1 and diam(A) ≤ C √ n(lnn), where H denotes the Hausdorff distance. These estimates are reasonably sharp. For every D > 0, we construct worst possible approximately c...
متن کاملON n-NORMED SPACES
Given ann-normed space withn≥ 2, we offer a simple way to derive an (n−1)norm from the n-norm and realize that any n-normed space is an (n−1)-normed space. We also show that, in certain cases, the (n−1)-norm can be derived from the n-norm in such a way that the convergence and completeness in the n-norm is equivalent to those in the derived (n− 1)-norm. Using this fact, we prove a fixed point t...
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: 1991
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1991-1059622-4