Displaying similar documents to “Functions that map cozerosets to cozerosets”

Čech-Stone-like compactifications for general topological spaces

Miroslav Hušek (1992)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

The problem whether every topological space X has a compactification Y such that every continuous mapping f from X into a compact space Z has a continuous extension from Y into Z is answered in the negative. For some spaces X such compactifications exist.

Finite-rank perturbations of positive operators and isometries

Man-Duen Choi, Pei Yuan Wu (2006)

Studia Mathematica

Similarity:

We completely characterize the ranks of A - B and A 1 / 2 - B 1 / 2 for operators A and B on a Hilbert space satisfying A ≥ B ≥ 0. Namely, let l and m be nonnegative integers or infinity. Then l = rank(A - B) and m = r a n k ( A 1 / 2 - B 1 / 2 ) for some operators A and B with A ≥ B ≥ 0 on a Hilbert space of dimension n (1 ≤ n ≤ ∞) if and only if l = m = 0 or 0 < l ≤ m ≤ n. In particular, this answers in the negative the question posed by C. Benhida whether for positive operators A and B the finiteness of rank(A - B) implies that...

Class groups of large ranks in biquadratic fields

Mahesh Kumar Ram (2024)

Czechoslovak Mathematical Journal

Similarity:

For any integer n > 1 , we provide a parametric family of biquadratic fields with class groups having n -rank at least 2. Moreover, in some cases, the n -rank is bigger than 4.

Class preserving mappings of equivalence systems

Ivan Chajda (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Similarity:

By an equivalence system is meant a couple 𝒜 = ( A , θ ) where A is a non-void set and θ is an equivalence on A . A mapping h of an equivalence system 𝒜 into ℬ is called a class preserving mapping if h ( [ a ] θ ) = [ h ( a ) ] θ ' for each a ∈ A . We will characterize class preserving mappings by means of permutability of θ with the equivalence Φ h induced by h .

Rational realization of the minimum ranks of nonnegative sign pattern matrices

Wei Fang, Wei Gao, Yubin Gao, Fei Gong, Guangming Jing, Zhongshan Li, Yan Ling Shao, Lihua Zhang (2016)

Czechoslovak Mathematical Journal

Similarity:

A sign pattern matrix (or nonnegative sign pattern matrix) is a matrix whose entries are from the set { + , - , 0 } ( { + , 0 } , respectively). The minimum rank (or rational minimum rank) of a sign pattern matrix 𝒜 is the minimum of the ranks of the matrices (rational matrices, respectively) whose entries have signs equal to the corresponding entries of 𝒜 . Using a correspondence between sign patterns with minimum rank r ≥ 2 and point-hyperplane configurations in ℝ r - 1 and Steinitz’s theorem on the rational realizability...

The 4-string braid group B 4 has property RD and exponential mesoscopic rank

Sylvain Barré, Mikaël Pichot (2011)

Bulletin de la Société Mathématique de France

Similarity:

We prove that the braid group B 4 on 4 strings, its central quotient B 4 / 〈 z 〉 , and the automorphism group Aut ( F 2 ) of the free group F 2 on 2 generators, have the property RD of Haagerup–Jolissaint. We also prove that the braid group B 4 is a group of intermediate mesoscopic rank (of dimension 3). More precisely, we show that the above three groups have exponential mesoscopic rank, i.e., that they contain exponentially many large flat balls which are not included in flats.