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Equality of Dimensions for Some Paracompact $$\sigma$$ -Spaces

Математические заметки, 2023
The equality of the dimensions $$\operatorname{Ind}X$$ and $$\operatorname{dim}X$$ of a first countable paracompact $$\sigma$$ -space $$X$$ with a 1-continuous semimetric is proved. A partial positive answer to A. V.
I. M. Leibo
semanticscholar   +1 more source

On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces

Mathematica Slovaca, 2023
ABSTRACTWe provide an overview of the known problem on the existence of a bi-Lipschitz equivalent metric with respect to a given quasi-ultrametric, revisiting known results and counterexamples in an unified approach based on the existence of a relaxed polygonal inequality. We present new proofs and characterizations of classical results using different
Caruso, Andrea Orazio   +1 more
openaire   +2 more sources

Caristi’s fixed point theorem in semimetric spaces

Journal of Fixed Point Theory and Applications, 2018
In [Lect. Notes Math. 490, 74--83 (1975; Zbl 0315.54052)], \textit{J. Caristi} and \textit{W. A. Kirk} proved an interesting fixed point theorem in complete metric space for $T$ satisfying a special condition. This result was extended by \textit{W. A. Kirk} and \textit{N. Shahzad} [J. Fixed Point Theory Appl. 17, No. 3, 541--555 (2015; Zbl 1326.54045)]
openaire   +1 more source

Vehicular air-bag control based on energy, momentum, and semimetric spaces

IEEE Transactions on Vehicular Technology, 2000
Described in this paper is a geometric control algorithm for quantifying crash severity, distinguishing crash configurations, and activating air bags during collisions. Its conceptual function and calibration depend on energy, momentum, and semimetric spaces.
R. Barnard, M. Riesner
openaire   +1 more source

Interval semimetric spaces for approximate distances

2005
In accordance with the ideas of Interval Analysis, a notion of interval-valued semimetric space is proposed. Also, the possibility of applying the resulting theory to some chapters of Computer Science is examined.
COPPOLA, CRISTINA, PACELLI, TIZIANA
openaire   +2 more sources

Convergent sequences in semimetric spaces

Publicationes Mathematicae Debrecen, 2022
openaire   +2 more sources

The biofilm matrix: multitasking in a shared space

Nature Reviews Microbiology, 2022
Hans-Curt Flemming   +2 more
exaly  

Responsive materials architected in space and time

Nature Reviews Materials, 2022
Xiaoxing Xia   +2 more
exaly  

Mappings contracting the total pairwise distances in semimetric spaces with triangle functions: Periodic and multiple fixed points

Ukrainian Mathematical Bulletin
This paper extends a recently introduced class of mappings contracting the total pairwise distances - an n-point extension of the Banach contraction principle - within the framework of semimetric spaces, employing triangle functions as defined by Bessenyei and Páles in [13].
Ravindra K. Bisht, Evgen O. Petrov
openaire   +1 more source

Cosmology with the Laser Interferometer Space Antenna

Living Reviews in Relativity, 2023
Germano Nardini
exaly  

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