Closed graph property in Alexandroff spaces
Abstract
In the following text we show if \(X\) is an Alexandroff space, then \(f:X\to Y\) has closed graph if and only if it has constant closed value on each connected component of \(X\). Moreover, if \(X\) is an Alexandroff space and \(f:X\to Y\) has closed graph, then \(f:X\to Y\) is continuous. As a matter of fact, the number of maps which have closed graph from an Alexandroff space \(X\) to a topological space \(Y\) depends just on the number of connected components of \(X\) and the number of closed points of \(Y\).
Fields of Study & Subjects
Digital Image Processing Techniques
Advanced Topology and Set Theory
Topological and Geometric Data Analysis
Publication details
- Journal / source
- Cubo
- Volume
- 28
- Issue
- 3
- Pages
- 429–429
- Publication date
- 1 September 2026