Displaying similar documents to “Free Power or Width of some Kinds of Mathematical Structures”

Fixed-point free maps of Euclidean spaces

R. Z. Buzyakova, A. Chigogidze (2011)

Fundamenta Mathematicae

Similarity:

Our main result states that every fixed-point free continuous self-map of ℝⁿ is colorable. This result can be reformulated as follows: A continuous map f: ℝⁿ → ℝⁿ is fixed-point free iff f̃: βℝⁿ → βℝⁿ is fixed-point free. We also obtain a generalization of this fact and present some examples

Sums and differences of power-free numbers

Julia Brandes (2015)

Acta Arithmetica

Similarity:

We employ a generalised version of Heath-Brown's square sieve in order to establish an asymptotic estimate of the number of solutions a, b ∈ ℕ to the equations a + b = n and a - b = n, where a is k-free and b is l-free. This is the first time that this problem has been studied with distinct powers k and l.

On the Existence of Free Ultrafilters on ω and on Russell-sets in ZF

Eleftherios Tachtsis (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

In ZF (i.e. Zermelo-Fraenkel set theory without the Axiom of Choice AC), we investigate the relationship between UF(ω) (there exists a free ultrafilter on ω) and the statements "there exists a free ultrafilter on every Russell-set" and "there exists a Russell-set A and a free ultrafilter ℱ on A". We establish the following results: 1. UF(ω) implies that there exists a free ultrafilter on every Russell-set. The implication is not reversible in ZF. 2. The...

Supersolvable orders and inductively free arrangements

Ruimei Gao, Xiupeng Cui, Zhe Li (2017)

Open Mathematics

Similarity:

In this paper, we define the supersolvable order of hyperplanes in a supersolvable arrangement, and obtain a class of inductively free arrangements according to this order. Our main results improve the conclusion that every supersolvable arrangement is inductively free. In addition, we assert that the inductively free arrangement with the required induction table is supersolvable.