We introduce the moduli space of quasi-parabolic $SL(2,\mathbb{C})$-Higgs bundles over a compact Riemann surface $\Sigma$ and consider natural involution, studying its fixed point locus when is $\mathbb{C} \mathbb{P}^1$ establishing an identification with null polygons in Minkowski $3$-space.

This paper concerns curves on non-commutative schemes, hereafter called quasi-schemes. A quasi-scheme X is identiied with the category ModX of quasi-coherent sheaves on it. Let X be a quasi-scheme having a regularly embedded hypersurface Y. Let C be a curve on X which is in \good posi-tion" with respect to Y (see Deenition 5.1)|this deenition includes a requirement that X be far from commutativ...

C. Akemann and G.K. Pedersen [Duke Math. J. 40 (1973), 785– 795.] defined three concepts of semicontinuity for self-adjoint elements of A∗∗, the enveloping von Neumann algebra of a C∗-algebra A. We give the basic properties of the analogous concepts for elements of pA∗∗p, where p is a closed projection in A∗∗. In other words, in place of affine functionals on Q, the quasi–state space of A, we c...

In this note we show that any k-CNF which can be refuted by a quasi-polynomial Res(polylog) refutation has a “narrow” refutation in Res (i.e., of poly-logarithmic width). Notice that while Res(polylog) is a complete proof system, this is not the case for Res if we ask for a narrow refutation. In particular is not even possible to express all CNFs with narrow clauses. But even for constant width...

This study involves new notions of continuity mapping between quasi-cone metrics spaces (QCMSs), cone metric (CMSs), and vice versa. The relation all were thoroughly studied supported with the help examples. In addition, these continuities compared various types two QCMSs. are

We study the coarse geometry of the Teichmüller space of a compact surface in the Teichmüller metric. We show that this admits a ternary operation, natural up to bounded distance, which endows the space with the structure of a coarse median space whose rank is equal to the complexity of the surface. We deduce that Teichmüller space satisfies a coarse quadratic isoperimetric inequality. We descr...

Extending the well-known result that every fuzzy metric space, in the sense of Kramosil and Michalek, has a completion which is unique up to isometry, we show that every KM-fuzzy quasi-metric space has a bicompletion which is unique up to isometry, and deduce that for each KM-fuzzy quasi-metric space, the completion of its induced fuzzy metric space coincides with the fuzzy metric space induced...

We introduce a new class of functions called θ-precontinuous functions which is contained in the class of weakly precontinuous (or almost weakly continuous) functions and contains the class of almost precontinuous functions. It is shown that the θprecontinuous image of a p-closed space is quasi H-closed. 2000 Mathematics Subject Classification. 54C08.

A subset E of a metric space (X, d) is totally bounded if and only if any sequence of points in E has a Cauchy subsequence. We call a sequence (xn) statistically quasiCauchy if st − limn→∞ d(xn+1, xn) = 0, and lacunary statistically quasi-Cauchy if Sθ − limn→∞ d(xn+1, xn) = 0.Weprove that a subset E of ametric space is totally bounded if and only if any sequence of points in E has a subsequence...

We introduce two kinds of quasi-inner functions. Since every rationally invariant subspace for a shift operator SK on a vector-valued Hardy space H(Ω, K) is generated by a quasi-inner function, we also provide relationships of quasi-inner functions by comparing rationally invariant subspaces generated by them. Furthermore, we discuss fundamental properties of quasi-inner functions, and quasi-in...