A characterization of order topologies by means of minimal $T\sb{0}$-topologies
نویسندگان
چکیده
منابع مشابه
A Characterization of Order Topologies by Means of Minimal 7vtopologies
In this article we give a purely topological characterization for a topology 3 on a set X to be the order topology with respect to some linear order R on X, as follows. A topology 3 on a set X is an order topology iff (X, 3) is a TVspace and 3 is the least upper bound of two minimal 7Vtopologies [Theorem 1 ]. From this we deduce a purely topological description of the usual topology on the set ...
متن کاملMinimal and High Order Neural Network Topologies 1 E. Fiesler Minimal and High Order Neural Network Topologies Simtec '93 2
One of the main goals of current neural network research consists in nding the optimal network topology for a given problem. Several methods have been proposed, but a mutual comparison of the resulting topologies remains a problem until proven minimal topologies are found. This paper describes a straightforward method for nding the minimal feed-forward topology for completely deened problems, b...
متن کاملCombinatorial Spaces And Order Topologies
An archetypal problem discussed in computer science is the problem of searching for a given number in a given set of numbers. Other than sequential search, the classic solution is to sort the list of numbers and then apply binary search. The binary search problem has a complexity of O(logN) for a list of N numbers while the sorting problem cannot be better than O(N) on any sequential computer f...
متن کاملA full characterization of evolutionary tree topologies
The topologies of evolutionary trees are shaped by the nature of the evolutionary process, but comparisons of trees from different processes are hindered by the challenge of completely describing tree topology. We present a full characterization of the topologies of rooted branching trees in a form that lends itself to natural tree comparisons. The resulting metric distinguishes trees from rand...
متن کاملPutting topologies on dp-minimal fields
4. If b ∈ acl(aS), then dp-rk(b/S) ≤ dp-rk(a/S). 5. dp-rk(ab/S) ≤ dp-rk(a/bS) + dp-rk(b/S). We work in a monster model C of a dp-minimal field (i.e., a field of dp-rank 1). “Models” will refer to small elementary substructures M C. We’ll write concatenation multiplicatively and multiplication using ·. We will assume that C is not strongly minimal. One already knows what strongly minimal fields ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0283767-7