AbstractWe present some combinatorial identities concerning the number T0(n,j) of all T0 topologies on n points with j open sets (which is also the number of all posets with n elements and j antichains). The average cardinality of (T0) topologies on n points is shown to be 2n2+O(log n)
AbstractFor subspaces X and Y of Q the notation X⩽hY means that X is homeomorphic to a subspace of Y...
AbstractLet pkn denote the number of unlabeled posets with n points and k unrelated pairs. We show t...
AbstractWe improve the results of Hartmanis (1958) and Schnare (1968,1969) by showing that, if n ⩾ 4...
AbstractWe present some combinatorial identities concerning the number T0(n,j) of all T0 topologies ...
AbstractRecent papers of Sharp [4] and Stephen [5] have shown that any finite topology with n points...
AbstractWe study the smallest possible number of points in a topological space having k open sets. E...
AbstractRecent papers of Sharp [4] and Stephen [5] have shown that any finite topology with n points...
AbstractWe study the smallest possible number of points in a topological space having k open sets. E...
AbstractLet S denote a finite set of cardinal n. The discrete topology on S contains 2n open sets; t...
AbstractFollowing the ideas of Sharp [2,3], we will give a partial answer to the question: “Let k be...
AbstractWe find an explicit formula for the number of graded partially ordered sets of rank h that c...
AbstractLet T be a finite topology. If P and Q are open sets of T (Q may be the null set) then P is ...
AbstractWe prove that for each integer l > 1 there exists a number r = r(l) > 1 such that every fini...
In set theory without the axiom of choice (AC), we observe new relations of the following statements...
The structure of the lattice of all subposets of a fixed poset is explored. This lattice is then use...
AbstractFor subspaces X and Y of Q the notation X⩽hY means that X is homeomorphic to a subspace of Y...
AbstractLet pkn denote the number of unlabeled posets with n points and k unrelated pairs. We show t...
AbstractWe improve the results of Hartmanis (1958) and Schnare (1968,1969) by showing that, if n ⩾ 4...
AbstractWe present some combinatorial identities concerning the number T0(n,j) of all T0 topologies ...
AbstractRecent papers of Sharp [4] and Stephen [5] have shown that any finite topology with n points...
AbstractWe study the smallest possible number of points in a topological space having k open sets. E...
AbstractRecent papers of Sharp [4] and Stephen [5] have shown that any finite topology with n points...
AbstractWe study the smallest possible number of points in a topological space having k open sets. E...
AbstractLet S denote a finite set of cardinal n. The discrete topology on S contains 2n open sets; t...
AbstractFollowing the ideas of Sharp [2,3], we will give a partial answer to the question: “Let k be...
AbstractWe find an explicit formula for the number of graded partially ordered sets of rank h that c...
AbstractLet T be a finite topology. If P and Q are open sets of T (Q may be the null set) then P is ...
AbstractWe prove that for each integer l > 1 there exists a number r = r(l) > 1 such that every fini...
In set theory without the axiom of choice (AC), we observe new relations of the following statements...
The structure of the lattice of all subposets of a fixed poset is explored. This lattice is then use...
AbstractFor subspaces X and Y of Q the notation X⩽hY means that X is homeomorphic to a subspace of Y...
AbstractLet pkn denote the number of unlabeled posets with n points and k unrelated pairs. We show t...
AbstractWe improve the results of Hartmanis (1958) and Schnare (1968,1969) by showing that, if n ⩾ 4...
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