ALEXANDROFF TOPOLOGY PDF

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

By using gopology site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Now, it is clear that Alexandrov topology is at least as big as the upper topology as every principle upper set is indeed an upper set, while the converse need not hold. Since the upper topology will have all the principle upper sets as open sets, wouldn’t then the arbitrary union of these open sets will end up generating the whole Alexandrov topology, as every upper set is a union of some set of principle upper sets?

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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

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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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