Orderability of subspaces of well-orderable topological spaces

We will show that all subspaces of well-ordered spaces are orderable, and we will characterize the well-orderability of subspaces of well-ordered spaces.     

Decomposing topological spaces into two rigid homeomorphic subspaces

We prove thatR can be split into two homeomorphic parts each of which has no autohomeomorphism except the identity. Moreover, this holds for many separable normed vector spaces over the rationals. The author thanks Azriel Levy for completely rewriting this paper.     

Partition theorems for subspaces of vector spaces

The principal result of this paper provides a nearly complete answer to the following question. For which cardinal numbers $\text{t}$, $\text{m}$, $\text{n}$, $\text{q}$ and $\text{r}$ is it true that whenever the $\text{t}$-dimensional subspaces of an $\text{n}$-dimensional vector space V over a field of $\text{q}$ elements are partitioned into $\text{r}$ classes, there must be some $\text{m}$-dimensional subspace of V, all of whose $\text{t}$-dimensional subspaces lie in the same class? This question is answered completely if $\text{r}$ ≤ $\text{N}$₀. The contributions of this paper are in the form of negative answers, since it turns out that all affirmative answers (which we have) were already known or easily deducible from known results.     

Fuzzy topological vector spaces I

Some of the properties of fuzzy topological vector spaces are investigated. Also, there are given necessary and sufficient conditions for a family of fuzzy sets, in a vector space E, to be the family of all neighborhoods of zero for a fuzzy linear topology.     

Partitions of finite vector spaces into subspaces

Let V_n(q) denote a vector space of dimension n over the field with q elements. A set of subspaces of V_n(q) is a partition of V_n(q) if every nonzero element of V_n(q) is contained in exactly one element of . Suppose there exists a partition of V_n(q) into x_i subspaces of dimension n_i, 1 ≤ i ≤ k. Then x₁, …, x_k satisfy the Diophantine equation . However, not every solution of the Diophantine equation corresponds to a partition of V_n(q). In this article, we show that there exists a partition of V_n(2) into x subspaces of dimension 3 and y subspaces of dimension 2 if and only if 7x + 3y = 2ⁿ ? 1 and y ≠ 1. In doing so, we introduce techniques useful in constructing further partitions. We also show that partitions of V_n(q) induce uniformly resolvable designs on qⁿ points. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 329–341, 2008     

Fuzzy topological vector spaces II

Some of the properties of the fuzzy seminormed and fuzzy normed spaces are studied. Also, the notion of a bornological fuzzy linear space is given and some of the properties of such a space are investigated.     

Sequential convergence in topological vector spaces

For a given linear topology , on a vector spaceE, the finest linear topology having the same convergent sequences, and the finest linear topology onE having the same precompact sets, are investigated. Also, the sequentially bornological spaces and the sequentially barreled spaces are introduced and some of their properties are studied.     

Semistable laws on topological vector spaces

Summary In this paper we discuss three types of results: Firstly, we present two Lévy-Hinin type representations of Poisson type infinitely divisible (i.d.) laws on certain topological vector (TV) spaces; one of these complements a known representation due to Dettweiler. Secondly, we define and characterize r-semistable laws on locally convex TV spaces and also obtain good representation of their characteristic functions. Finally, we discuss the existence and the continuity of the semigroup { _tt>0} of i.d. laws on locally convex TV spaces. These complement similar known results of Siebert.The research of this author is partially supported by the Office of Naval Research under contract No. N0014-78-C-0468