In this paper we present new forms of the classical separation axioms on topological spaces. Our constructions generate a method to refine separation properties when passing to the quotient space and our results may be useful in the study of algebraic topological structures, such as topological groups and topological vector spaces. AMS subject classification: 54D10, 54D15, 54H11, 54H13.

Let X be a completely regular Hausdorff space, E a Hausdorff topological vector space, CL(E) the algebra of continuous operators on E, V a Nachbin family on X and F ⊆ CVb(X,E) a topological vector space (for a given topology). If π : X → CL(E) is a mapping and f ∈ F , let Mπ(f)(x) := π(x)f(x). In this paper we give necessary and sufficient conditions for the induced linear mapping Mπ to be a mu...

We establish topological properties of the topological symmetric inverse semigroup of finite transformations I n λ of the rank 6 n. We show that the topological inverse semigroup I n λ is algebraically closed in the class of topological inverse semigroups. Many topologists established topological property of topological spaces of partial continuous maps PC (X, Y ) from a topological space X int...

Andrew J. Hanson Computer Science Department Indiana University Bloomington, IN 47405 [email protected] } Introduction } Our purpose here is to show how the quaternion formalism can be applied with great success not only to the interpolation between coordinate frames, but also to a remarkably elegant description of the evolving coordinate-frame geometry of curves. Speci c applications of th...

Elementary mathematical concepts from linear algebra are used to develop an independent theory for non-directed bond graphs. The dejinition of a bond graph is given and its structure as a combinatorial object is studied. This is accomplished by constructing a vector space, called the bond space of the bond graph. Topological information is encoded in the bond graph by dejining a subspace of the...

In this paper, the Urysohn, completely Hausdorff and completely regular axioms in $L$-topological spaces are generalized to $L$-fuzzy topological spaces. Each $L$-fuzzy topological space can be regarded to be Urysohn, completely Hausdorff and completely regular tosome degree. Some properties of them are investigated. The relations among them and $T_2$ in $L$-fuzzy topological spaces are discussed.

Field theories with a S 2-valued unit vector field living on S 3 × IR space-time are investigated. The corresponding eikonal equation, which is known to provide an integrable sector for various sigma models in different spaces, is solved giving static as well as time-dependent multiply knotted configurations on S 3 with arbitrary values of the Hopf index. Using these results, we then find a set...

in this paper, some fundamental concepts are given relating to fuzzytopological spaces. then it is shown that there is a contravariant functorfrom the category of the pointed fuzzy topological spaces to the category ofgroups and homomorphisms. also the fuzzy topological spaces which are hopfspaces are investigated and it is shown that a pointed fuzzy toplogicalspace having the same homotopy typ...