Continuous

1. This is in fact equivalent to being continuous with respect to the Scott topology on the respective posets. (Web site)

Sober

1. Especially, the Scott topology is not necessarily sober. (Web site)

Continuous Functions

1. Both currying and apply are continuous functions in the Scott topology, and currying, together with apply, provide the adjoint.

Topology

1. We show that the Scott topology induces a topology for real-valued Lipschitz maps on Banach spaces which we call the L-topology.

Natural Topology

1. For example, the natural topology on Scott-Ershov domains is the Scott topology.

Finest Topology

1. The finest topology that is order consistent in the above sense for a given order ≤ is the Scott topology. (Web site)

Scott Topology

1. Hence any sober space with specialization order ≤ is finer than the upper topology and coarser than the Scott topology. (Web site)
2. There are some other examples of the Scott topology that are useful in analysis and will play a major role in this paper. (Web site)
3. The finest order consistent topology is the Scott topology, which is coarser than the Alexandrov topology. (Web site)

Categories

1. Finest Topology
2. Science > Mathematics > Topology > Alexandrov Topology
3. Natural Topology
4. Specialization Order
5. Coarser
6. Books about "Scott Topology" in Amazon.com
   

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