The set of real numbers with the cocountable topology has a bounded complete dcpo model
Dongsheng Zhao, Chong Shen, Xiaoyong Xi
Abstract
We construct a bounded complete dcpo P whose maximal point space is homeomorphic to the set R of all reals equipped with the cocountable topology, thereby answering an open problem. Using this dcpo, we obtain a new complete lattice whose Scott space is non-sober.
Create a lesson
Related papers
Fractal dimensions and quasisymmetric packing-minimalities of some homogeneous Moran sets
Pingping Liu, Chenyuan Jiang, Yanzhe Li
Proper classes of non-embeddable continua
Gerald Kuba
On Ist- convergence in the space of reals
Amar Kumar Banerjee, Khairul Hasan
Homogeneous linearly ordered spaces
Anton Lipin, Evgenii Reznichenko
A New Approach to Universal Measurability
Reznichenko E. A., Sadovnichiy Yu.
One-Point Metrizable Coarsenings: Gauges and Local Metric Preservation
Ahmad ja'afari kalvan, Ehsan Shahoseini