Tangency and orthogonality in metric spaces

• Autorzy: Pascali E.
• Języki publikacji: EN

Abstrakty

EN

We consider an abstract definition of tangency in metric spaces and study some of its properties. We introduce also a particular structure on metric spaces and define, with respect this structure, the notion of tangency and orthogonality. Some properties of continuous curves in such spaces are investigated.

Słowa kluczowe

EN

metric space; orthogonality; Banach space; continuous curves

PL

przestrzeń Banacha; przestrzeń metryczna; ortogonalność; krzywe ciągłe

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 437--449
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Pascali E.

• Departments of Mathematics "Ennio de Giorgi", University of Lecce, C.P. 193, 73100, Lecce, Italy

Bibliografia

• [1] J. Alonso-C. Benitez, Orthogonality in normed linear spaces: A survey part I, IO; Extracta Math. 3 n.1 (1988), 1-15 and 4 n. 3 (1989), 121-131.
• [2] D. Amir, Characterisation of Inner Product Spaces, Birkauser, 1986.
• [3] L.M. Blumenthal, Distance Geometry, Oxford Univ. Press, 1953.
• [4] H. Buseman, The foundation of Minkowskian Geometry, Comm. Math. Helv. 24 (1950), 156-187.
• [5] G. Ewald-Le Roy, M. Kelly, Tangents in real Banach Spaces, J. Math. 203 h. 3/4 (1960), 160-173.
• [6] H. Federer, Geometric Measure Theory, Springer, 1969.
• [7] S. Gołąb, Z. Moszner, Sur le contact des courbes dans les espaces metriques generaux, Colloq. Math. 10 fasc. 2 (1963), 305-311.
• [8] J. Grochulski, T. Konik, M. Tkacz, On the tangency of sets in metric spaces Ann. Polon. Math. 38 (1980) 121-136.
• [9] J. Grochulski, T. Konik, M. Tkacz, On some relations of tangency of arcs in metric spaces, Demonstratio Math. 11 (1978), 567-582.
• [10] J. Grochulski, T. Konik, M. Tkacz, On the equivalence of certain relations of tangency of arcs in metric spaces, Demonstratio Math. 11 (1978), 261-271.
• [11] C. Pauc, La méthod metric en calcul des variations, Actualites Scientifiques et Industrielles, 885, Hermann & C (1941).
• [12] E. Pascali, Derivazione e spazi metrici, Preprint, Dip. di Mat. di Lecce, 3(1995), 1-20.
• [13] T. Konik, On the tangency of sets of some class in generalized metric spaces, Demonstratio Math. 22, 4 (1989), 1093-1107.
• [14] T. Konik, On the tangency of sets, Demonstratio Math. 22, 4 (1989), 737-746.
• [15] W. Waliszewski, On the tangency of sets in metric spaces, Colloq. Math. 151 (1966), 129-133.
• [16] W. Waliszewski, On the tangency of sets in generalized metric spaces, Ann. Polon. Math. 28 (1973), 275-284.