On maps: continuous, closed, perfect, and with closed graph
نویسندگان
چکیده
منابع مشابه
Continuous Maps on Digital Simple Closed Curves
We give digital analogues of classical theorems of topology for continuous functions defined on spheres, for digital simple closed curves. In particular, we show the following: 1) A digital simple closed curve S of more than 4 points is not contractible, i.e., its identity map is not nullhomotopic in S ; 2) Let X and Y be digital simple closed curves, each symmetric with respect to the origin, ...
متن کاملRc-continuous Functions and Functions with Rc-strongly Closed Graph
The family of regular closed subsets of a topological space is used to introduce two concepts concerning a function f from a space X to a space Y . The first of them is the notion of f being rc-continuous. One of the established results states that a space Y is extremally disconnected if and only if each continuous function from a space X to Y is rc-continuous. The second concept studied is the...
متن کاملBanach's Continuous Inverse Theorem and Closed Graph Theorem
The terminology and notation used here have been introduced in the following articles: [3], [4], [2], [15], [11], [14], [1], [5], [13], [12], [19], [20], [16], [7], [17], [8], [18], [9], and [6]. Let X, Y be non empty normed structures, let x be a point of X, and let y be a point of Y . Then 〈x, y〉 is a point of X × Y. Let X, Y be non empty normed structures, let s1 be a sequence of X, and let ...
متن کاملOn Closed Operators with Closed Range1
It is well-known that if T is an everywhere defined bounded operator on a Banach space X to a Banach space Y and T* is its adjoint, then the range R(T*) of T* is closed in X* if and only if the range R(T) of T is closed in Y (cf. [2, pp. 487-489]). The object of this note is to establish this result for closed but possibly unbounded operators. This result, for the unbounded case, is of great ut...
متن کاملA Note on Closed Graph Theorems
We give a common generalisation of the closed graph theorems of De Wilde and of Popa.
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 1997
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171297000537