a set for which a metric is defined between every pair of points
metric space in American English
noun
Math
a space with a metric defined on it
Word origin
[1925–30]This word is first recorded in the period 1925–30. Other words that entered Englishat around the same time include: Nazi, buildup, recycle, reflex camera, runout
Examples of 'metric space' in a sentence
metric space
Consider a continuous function on a metric space.
V. V. Motreanu 2013, 'Minimax Results with Respect to Different Altitudes in the Situation of Linking',Abstract and Applied Analysishttp://dx.doi.org/10.1155/2013/781746. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Several notions of convergence for subsets of metric space appear in the literature.
Ömer Kişi, Fatih Nuray 2013, 'New Convergence Definitions for Sequences of Sets', Abstract and Applied Analysishttp://dx.doi.org/10.1155/2013/852796. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We show that such contractions have fixed points in a complete probabilistic metric space.
Choudhury B. S., Bhandari S. K. 2016, 'P-Cyclic C-Contraction Result in Menger Spaces Using a Control Function', Demonstratio Mathematicahttp://www.degruyter.com/view/j/dema.2016.49.issue-2/dema-2016-0018/dema-2016-0018.xml?format=INT. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
For this, we introduce the notion of $c_0$-triangular fuzzy metric space.
Masoomeh Hezarjaribi 2018, 'Meir-Keeler Type Contraction Mappings in $c_0$-triangular Fuzzy Metric Spaces', Sahand Communications in Mathematical Analysishttp://scma.maragheh.ac.ir/article_31436_7931223a921acacbf9af5f50b37f2216.pdf. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Our main results cannot be specifically attained from the corresponding metric space versions.
Haitham Qawaqneh, Mohd Noorani, Wasfi Shatanawi, Habes Alsamir 2018, 'Common Fixed Point Theorems for Generalized Geraghty (α,ψ,ϕ)-QuasiContraction Type Mapping in Partially Ordered Metric-Like Spaces', Axiomshttps://www.mdpi.com/2075-1680/7/4/74. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
Therefore, they can be measured by metric in a sense of metric space theory.
Masárová Renáta 2014, 'Fréchet Metric for Space of Binary Coded Software', Research Papers. Faculty of Materials Science and Technology. Slovak University ofTechnology in Trnavahttp://www.degruyter.com/view/j/rput.2014.22.issue-35/rput-2014-0030/rput-2014-0030.xml?format=INT. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)
We show that the proposed measure forms a metric space and can be computed efficiently.
Yong-Hyuk Kim, Yourim Yoon 2015, 'Linkage-Based Distance Metric in the Search Space of Genetic Algorithms', Mathematical Problems in Engineeringhttp://dx.doi.org/10.1155/2015/680624. Retrieved from DOAJ CC BY 4.0 (https://creativecommons.org/licenses/by-sa/4.0/legalcode)