In this paper we characterize when the semi-commutator TfTg − Tfg of two Toeplitz operators Tf and Tg on the Hardy space of the bidisc is zero. We also show that there is no nonzero finite rank semi-commutator on the bidisc. Furthermore explicit examples of compact semi-commutators with symbols continuous on the bitorus T 2 are given.

Ever since the introduction of fuzzy sets by L. A. Zadeh [14], the fuzzy concept has invaded almost all branches of Mathematics. The concept of fuzzy topological space was introduced and developed by C.L. Chang [3] and since then many fuzzy topologists [1,6-13] have extended various notions in classical topology to fuzzy topological spaces. The concept of somewhat continuous functions was intro...

It is a consequence of known results^) that any compact light open mapping / of one two-dimensional manifold A into another one B has a definite finite degree k(f), that is, there is an integer k(f) such that for each y£j(A),f~l(y) contains exactly k(f) points provided the points of/_l(y) are counted with multiplicity in an obvious manner. Further, considered as a function on the subset O of co...

The original aim of this paper is to construct a graph associated to a vector space. By inspiration of the classical definition for the Cayley graph related to a group we define Cayley graph of a vector space. The vector space Cayley graph ${rm Cay(mathcal{V},S)}$ is a graph with the vertex set the whole vectors of the vector space $mathcal{V}$ and two vectors $v_1,v_2$ join by an edge whenever...

Open set classification (OSC) tackles the problem of determining whether data are in-class or out-of-class during inference, when only provided with a examples at training time. Traditional OSC methods usually train discriminative generative models owned data, and then utilize pre-trained to classify test directly. However, these always suffer from embedding confusion problem, i.e., partial ins...

in this paper, we introduce λκ−closed sets and study its properties in generalized topological spaces.

Every lower semi-continuous closed-and-convex valued mapping Φ : X → 2 , where X is a Σ-product of metrizable spaces and Y is a Hilbert space, has a single-valued continuous selection. This improves an earlier result of the author.

We introduce a natural topology on the space of left orderings of an arbitrary semi-group G. We prove that this space is always compact and that for free abelian groups it is homeomorphic to the Cantor set. We use our topological approach to provide a simple proof of the existence of universal Gröbner bases. 1. Orderings for semi-groups Given a semi-group G (ie. a set with an associative binary...