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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 발행연도
- 2015.1
- 수록면
- 449 - 472 (24page)
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Let X be a nonempty set and mathcal F(X) be the set of nonempty finite subsets of X. The paper deals with the extended metrics τ : F(X)→ R recently introduced by Peter Balk. Balk's metrics and their restriction to the family of sets A with |A| n make possible to consider "distance functions" with n variables and related them quantities. In particular, we study such type generalized diameters diam tn and find conditions under which B ↦ diam τn B is a Balk's metric. We prove the necessary and sufficient conditions under which the restriction τ to the set of A ∈ F(X) with |A| 3 is a symmetric G-metric. An infinitesimal analog for extended by Balk metrics is constructed.
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참고문헌 (21)
참고문헌 신청
A. A. Dovgoshey / 2012 / D. V. Dordovskyi, An ultrametricity condition for pretangent spaces / Math. Notes 92 (7) : 43 ~ 50
B. C. Dhage / 1992 / Generalized metric space and mapping with 칧ed point / Bull. Calcutta Math. Soc 84 (4) : 329 ~ 336
D. Dordovskyi. / 2011 / Diameter and Diametrical Pairs of Points in Ultrametric Spaces, p-Adic Numbers / Ultrametric Anal. App 3 (4) : 253 ~ 262
Dmitrii V. Dordovski / 2011 / Metric tangent spaces to Euclidean spaces / J. Math. Sci. (N. Y. ) 179 (2) : 229 ~ 244
F. Abdullayev. / 2011 / Metric spaces with unique pretangent spaces. Conditions of the uniqueness / Ann. Acad. Sci. Fenn. Math 36 : 353 ~ 392
B. C. Dhage / 1992 / Generalized metric space and mapping with 칧ed point / Bull. Calcutta Math. Soc 84 (4) : 329 ~ 336
D. Dordovskyi. / 2011 / Diameter and Diametrical Pairs of Points in Ultrametric Spaces, p-Adic Numbers / Ultrametric Anal. App 3 (4) : 253 ~ 262
Dmitrii V. Dordovski / 2011 / Metric tangent spaces to Euclidean spaces / J. Math. Sci. (N. Y. ) 179 (2) : 229 ~ 244
F. Abdullayev. / 2011 / Metric spaces with unique pretangent spaces. Conditions of the uniqueness / Ann. Acad. Sci. Fenn. Math 36 : 353 ~ 392
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