Normality of powers implies compactness

Compactness and Normality in Abstract Logics

Caicedo, X., Compactness and normality in abstract logics, Annals of Pure and Applied Logic 59 (1993) 33-43. We generalize a theorem of Mundici relating compactness of a regular logic L to a strong form of normality of the associated spaces of models. Moreover, it is shown that compactness is in fact equivalent to ordinary normality of the model spaces when L has uniform reduction for infinite ...

σ-Normality of Topological Spaces

Domination number of graph fractional powers

For any $k in mathbb{N}$, the $k$-subdivision of graph $G$ is a simple graph $G^{frac{1}{k}}$, which is constructed by replacing each edge of $G$ with a path of length $k$. In [Moharram N. Iradmusa, On colorings of graph fractional powers, Discrete Math., (310) 2010, No. 10-11, 1551-1556] the $m$th power of the $n$-subdivision of $G$ has been introduced as a fractional power of $G$, denoted by ...

Normality, Projective Normality and Egz Theorem

In this note, we prove that the projective normality of (P(V )/G,L), the celebrated theorem of Erdös-Ginzburg-Ziv and normality of an affine semigroup are all equivalent, where V is a finite dimensional representation of a finite cyclic group G over C and L is the descent of the line bundle O(1)⊗|G|.

Powers of Two Modulo Powers of Three

Since 2 is a primitive root of 3 for each positive integer m, the set of points {(n, 2 mod 3) : n > 0}, viewed as a subset of Z>0×Z>0 is bi-periodic, with minimal periods φ(3) (horizontally) and 3 (vertically). We show that if one considers the classes of n modulo 6, one obtains a finer structural classification. This result is presented within the context of the question of strong normality of...