Abstract
A topological space X is said to be unicoherent provided that it is connected and for every two closed connected sets A and B with X, which is equal to A⋃B, the intersection A∩B is connected. Euclidean spaces ℝn, cubes [0, 1]n for any positive integer n, spheres Sn for n ≥ 2, real projective spaces Pn(ℝ) also for n ≥ 2, Hilbert cube [0, 1]ω and solenoids are unicoherent, while the circle S1, the torus S1 ×S1 and the Mˆbius band are not. The notion of unicoherence is a special case of a general concept of multicoherence. The concept of unicoherence has been modified in several ways. A connected space X is said to be weakly unicoherent provided that for every two closed connected sets A and B, one of which is compact, if X = A ∪ B then A ∩ B is connected.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
