We present examples of phononic structures that beak four types of symmetry, namely timereversal symmetry, parity symmetry, chiral symmetry and particle-hole symmetry. The implications of symmetry breaking on the topology of the acoustic wave function in the space of its Eigen values are discussed. Particular attention is focused on the torsional topology of acoustic waves in periodic media in ...

Abstract In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved varying measures vaguely convergent.

In this paper we introduce the concept of (α, β, θ, ∂, I)-continuous mappings and prove that if α, β are operators on the topological space (X, τ) and θ, θ∗ , ∂ are operators on the topological space (Y, φ) and I a proper ideal on X, then a function f : X → Y is (α, β, θ ∧ θ∗, ∂, I)-continuous if and only if it is both (α, β, θ, ∂, I) -continuous and (α, β, θ∗, ∂, I)-continuous, generalizing a ...

We present a construction which shows that the Tiordered reflection (i ∈ {0, 1, 2}) of a partially ordered topological space (X, τ,≤) exists and is an ordered quotient of (X, τ,≤). We give an explicit construction of the T0-ordered reflection of an ordered topological space (X, τ,≤), and characterize ordered topological spaces whose T0-ordered reflection is T1-ordered. 2000 AMS Classification: ...

Let Xo and X, be two Banach spaces which are continuously embedded in a common Hausdort t topological vector space. An admissible operator for the pair (Xo, X,) is a linear operator whose domain contains the union of the two spaces and whose restrictions to Xi is a bounded operator on Xi ( i = 0 , 1). A space X is called an interpolation space for the pair (Xo, X,) if each admissible operator T...

A connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y , separately continuous function f : X ×Y →R and open set I ⊆R, the set f −1(I) is an Fσ-set) is studied. We show that every completely regular Baire space with the L-property and the countable chain condition is separable and c...

A theorem of Luxemburg and Zaanen on normed Riesz spaces (Theorem 2.4 below) and one of Nakano (Theorem 2.3 below) have been extended by the author in [1] to metrizable locally solid linear topological Riesz spaces. This note gives an example which shows they cannot be further extended to nonmetrizable Hausdorff locally solid linear topological Riesz spaces. 1. Notation and basic concepts. For ...

In this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $X$,  where $X$ is a $C$-distinguished topological space. Then, we show that their dual spaces can be identified in a natural way with certain spaces of Radon measures.