Graph intersection property
Abstract
A pair (X,Y) of topological spaces X and Y is said to have the graph intersection property provided that for each continuous function g: XY, if a connected subset of X Y projects onto the whole Y, then it intersect the graph of g. Various relations between this and other known properties related to mapping theory are studied.
In particular, it is proved that: 1) if a space X is completely regular and a space Y is an arcwise connected metric continuum distinct from an arc, then the pair (X,Y) has the graph intersection property if and only if X is hereditary disconnected; 2) if a connected space Y is fixed, then the graph intersection property holds for every pair (X,Y) if and only if there is a closed linear order on Y with minimal and maximal elements. Related results are obtained.
The authors retain all rights to the original work without any restrictions.
License for Published Contents
"Le Matematiche" published articlesa are distribuited with Creative Commons Attribution 4.0 International. You are free to copy, distribute and transmit the work, and to adapt the work. You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
License for Metadata
"Le Matematiche" published articles metadata are dedicated to the public domain by waiving all publisher's rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
No Fee Charging
No fee is required to complete the submission/review/publishing process of authors paper.
