Rudin, Chapter 4, Problem #3. The space L(T ) is separable since the trigonometric polynomials with complex coefficients whose real and imaginary parts are rational form a countable dense subset. (Denseness follows from Theorem 3.14 and Theorem 4.25; countability is clear since {e | n ∈ Z} is a countable basis of the trigonometric polynomials.) Meanwhile the space L(T ) is not separable. To see...

We consider Potts model hypersurfaces defined by the multivariate Tutte polynomial of graphs (Potts model partition function). We focus on the behavior of the number of points over finite fields for these hypersurfaces, in comparison with the graph hypersurfaces of perturbative quantum field theory defined by the Kirchhoff graph polynomial. We give a very simple example of the failure of the “f...

Consider a closed subgroup H of a locally compact group G together with a strongly continuous unitary representation u of H on a Hilbert space K. The construction of the induced representation uses these three ingredients to supply a new strongly continuous unitary representation ρ of the larger group G on a new Hilbert space K. Induced group representations for finite groups where first introd...

Soft ω-local indiscreetness as a weaker form of both soft local countability and is introduced. Then ω-regularity regularity defined investigated. Additionally, ω-T2 new topological property that lies strictly between T2 T1 It proved anti-local sufficient condition for equivalence ω-locally (resp. ω-regularity) locally ω-regularity). it the induced spaces indiscrete ω-regular, ω-T2) space are s...

Abstract We investigate the computational properties of basic mathematical notions pertaining to ${\mathbb R}\rightarrow {\mathbb R}$-functions and subsets R}$, like finiteness, countability, (absolute) continuity, bounded variation, suprema regularity. work in higher-order computability theory based on Kleene’s S1–S9 schemes. show that aforementioned italicised give rise two huge robust classe...

In this article we discuss the distribution of linking element -e- in NN-compounds Mooring Frisian, a mainland North Frisian dialect. Although is homophonous with regular plural ending -e and triggers allomorphy, argue against an equation ending. We propose that elements are semantically void augments or stem extensions, may optionally serve phonological (prosodic) and/or quasi-morphological fu...

Potentially all Japanese nouns are under-specified with respect to number and countability. To ask a user to interactively disambiguate each one is not feasible, and it can be impossible for a native speaker to do. Therefore it is important to disambiguate automatically. In addition, even if the system makes a mistake about number, it is rarely fatal. There are some ambiguities involved with th...

The directions of an infinite graph G are a tangle-like description its ends: they choice functions that choose component G−X for all finite vertex sets X⊆V(G) in compatible manner. Although every direction is induced by ray, there exist graphs not uniquely determined any countable subset their choices. We characterise these and countably counterparts terms star-like substructures or rays the g...