Ultradiversities and their spherical completeness
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Gholamreza H. Mehrabani
Abstract
Diversities are a generalization of metric spaces which associate a positive real number to every finite subset of the space. In this paper, we introduce ultradiversities which are themselves simultaneously diversities and a sort of generalization of ultrametric spaces. We also give the notion of spherical completeness for ultradiversities based on the balls defined in such spaces. In particular, with the help of nonexpansive mappings defined between ultradiversities, we show that an ultradiversity is spherically complete if and only if it is injective.
Acknowledgements
The authors would like to thank the reviewer for his/her valuable comments on this paper. The authors would also like to thank Pooya Haghmaram for his constructive comments on the main result of this paper.
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© 2020 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Optimal importance sampling for continuous Gaussian fields
- Orlicz lacunary sequence spaces of 𝑙-fractional difference operators
- Adjoint of generalized Cesáro operators on analytic function spaces
- Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
- Images of circles, lines, balls and half-planes under Möbius transformations
- Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space
- Ultradiversities and their spherical completeness
- Controllability of multi-term time-fractional differential systems with state-dependent delay
- On integrals associated with the free particle wave packet
- On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order
- Comparison estimates on the first eigenvalue of a quasilinear elliptic system
- Stability analysis of conformable fractional-order nonlinear systems depending on a parameter
- A nonlocal problem for a differential operator of even order with involution
- Large deviations for longest runs in Markov chains
- A computational method for time fractional partial integro-differential equations
Artikel in diesem Heft
- Frontmatter
- Optimal importance sampling for continuous Gaussian fields
- Orlicz lacunary sequence spaces of 𝑙-fractional difference operators
- Adjoint of generalized Cesáro operators on analytic function spaces
- Positive and nontrivial solutions to a system of first-order impulsive nonlocal boundary value problems with sign changing nonlinearities
- Images of circles, lines, balls and half-planes under Möbius transformations
- Convergence theorems for generalized hemicontractive mapping in p-uniformly convex metric space
- Ultradiversities and their spherical completeness
- Controllability of multi-term time-fractional differential systems with state-dependent delay
- On integrals associated with the free particle wave packet
- On existence and uniqueness results for iterative mixed integrodifferential equation of fractional order
- Comparison estimates on the first eigenvalue of a quasilinear elliptic system
- Stability analysis of conformable fractional-order nonlinear systems depending on a parameter
- A nonlocal problem for a differential operator of even order with involution
- Large deviations for longest runs in Markov chains
- A computational method for time fractional partial integro-differential equations
