This work grew out of an attempt to generalize the construction of Chern-Simons invariants. In this paper, we associate a geometric invariant to the space of flat connection on a SU(2)-bundle on a compact Riemann surface and relate it to the energy of harmonic functions on the surface. Our set up is as follows. Let G = SU(2) and M be a compact Riemann surface and E ~ M be the trivial G-bundle. ...

In this paper, the concepts of derived sets and derived operators are generalized to $(L, M)$-fuzzy topological spaces and their characterizations are given.What is more, it is shown that the category of stratified $(L, M)$-fuzzy topological spaces,the category of stratified $(L, M)$-fuzzy closure spaces and the category of stratified $(L, M)$-fuzzy quasi-neighborhood spaces are all isomorphic ...

 The main purpose of this paper is to study the existence of afixed point in locally convex topology generated by fuzzy n-normed spaces.We prove our main results, a fixed point theorem for a self mapping and acommon xed point theorem for a pair of weakly compatible mappings inlocally convex topology generated by fuzzy n-normed spaces. Also we givesome remarks in locally convex topology generate...

We find some statements in the language of asymmetric topology and continuous partial orders which are equivalent to the statements κ < m or κ < p. We think of asymmetric topology as those parts of topology in which the specialization order, x ≤ y if and only if x ∈ c{y}, need not be symmetric. (See [5] for some of the motivations.) Martin’s Axiom has many equivalent statements, consequences, a...

We prove a characterization theorem for the unit polydisc ∆ ⊂ C in the spirit of a recent result due to Kodama and Shimizu. We show that if M is a connected n-dimensional complex manifold such that (i) the group Aut(M) of holomorphic automorphisms of M acts on M with compact isotropy subgroups, and (ii) Aut(M) and Aut(∆) are isomorphic as topological groups equipped with the compact-open topolo...

Given an arbitrary ideal f on the real numbers, two topologies are denned that are both finer than the ordinary topology. There are nonmeasurable, non-Baire sets that are open in all of these topologies, independent of f . This shows why the restriction to Baire sets is necessary in the usual definition of the ./"-density topology. It appears to be difficult to find such restrictions in the cas...

‎Assume that $A$ is a Banach algebra‎. ‎We define the‎ ‎$beta-$topology and the $gamma-$topology on the space $QM_{el}(A^{*})$ of all bounded extended left quasi-multipliers of $A^{*}.$‎ ‎We establish further properties of $(QM_{el}(A^{*}),gamma)$ when $A$ is a $C^{*}-$algebra‎. ‎In particular‎, ‎we characterize the $gamma-$dual‎ ‎of $QM_{el}(A^{*})$ and prove that $(QM_{el}(A^{*}),gamma)^{*},$...

In this article, the ant colony method is utilized for topology optimization of space structures. Strain energy of the structure is minimized while the material volume is limited to a certain amount. In other words, the stiffest possible structure is sought when certain given materials are used. In addition, a noise cleaning technique is addressed to prevent undesirable members in optimum topol...

TOPOLOGY IN MEDICAL IMAGE SEGMENTATION M. C. Jobin Christ1 and R. M. S. Parvathi2 1Lecturer, Department of Biomedical Engineering, Adhiyamaan College of Engineering, Hosur, Tamilnadu, India. E-mail: [email protected] 2Principal, Sengunthar College of Engineering for Women, Tiruchencode, Tamilnadu, India. E-mail: [email protected] Topology is the mathematical study of the properties that...