In this paper, we associate a topology to G, called graphic topology of G and we show that it is an Alexandroff topology, i.e. a topology in which intersec- tion of. Alexandroff spaces, preorders, and partial orders. 4. 3. Continuous A-space, then the closed subsets of X give it a new A-space topology. We write. Xop for X. trate on the definition of the T0-Alexandroff space and some of its topological . the Scott topology and the Alexandroff topology on finite sets and in general.
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The specialisation topology
Or, upper topology is simply presented with upper sets and their intersections, and nothing more?
I am obviously missing something here. The problem apexandroff that your definition of the upper topology is wrong: Under your definitions, both topologies are the same. Note that the upper sets are non only a base, they form the whole topology.
And the principal upper sets are only only a subbase, they from a base. I have also found another definition of the upper topology: This topology may be strictly coarser, but they are the same if the order is linear.
Alexandrov topology – Wikipedia
Home Questions Tags Users Unanswered. Alexandrov topology Ask Question. But I have the following confusion. Scott k 38 They are not the same for every linear order. Sign up or log in Sign up using Google.
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