We show that the Galois group Gal(Q̄/Q) operates faithfully on the set of connected components of the moduli spaces of surfaces of general type, and also that for each element σ ∈ Gal(Q̄/Q) different from the identity and from complex conjugation, there is a surface of general type such that X and the Galois conjugate variety Xσ have nonisomorphic fundamental groups. The result was announced by t...

Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Ha...

In this work, we introduce notion of connectedness on fuzzy soft topological spaces and present fundamentals properties. We also investigate effect to fuzzy soft connectedness. Moreover, $C_i$-connectedness which plays an important role in fuzzy topological space extend to fuzzy soft topological spaces.