A note on the core topology and three other ones

• Autorzy: Jankowski L. , Marlewski A.
• Języki publikacji: EN

Abstrakty

EN

In the paper there are considered the topologies defined in real linear spaces: the core topology, the topology generated by the family of directionally continuous functions, and the topology defined by Klee in [7]. The notion of the last one is extended to infinite dimensional case by means of the finite topology investigated by Kakutani and Klee [5]. Some properties of the finite topology are proved. The main result says that every one of considered topologies contain essentially the next one in the order listed above.

Słowa kluczowe

EN

topology; real linear space

PL

topologia; przestrzeń liniowa

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2005
• Tom: Nr 36
• Strony: 49--63
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Jankowski L.

• Institute of Mathematics, Poznań University of Technology Piotrowo 3A, 60-965 Poznań, Poland

autor

Marlewski A.

• Institute of Mathematics, Poznań University of Technology Piotrowo 3A, 60-965 Poznań, Poland

Bibliografia

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• [2] Horbaczewska G., Core density topologies, Real Analysis Exchange, 20(2)(1994/95), 416-417.
• [3] Horbaczewska G., Some modifications of the core topology on the plane. Real Analysis Exchange, 24(l)(1998/99), 185-204.
• [4] Jankowski L., Some properties of the core topologies, Comm. Math., XIX (1977), 239-247.
• [5] Kakutani S., Klee V., The finite topology of a linear space. Arch. Math., 14(1963), 55-58.
• [6] Klee V.L., Convex sets in linear spaces, Duke Math. J., 18(1951), 444-466.
• [7] Klee V.L., Some finite-dimensional affine topological spaces, Portugal Math., 14(1955), 27-30.
• [8] Klose J., a note on the core topology used in optimization. Optimization, 23(1992), 27-40.
• [9] Kuczma M., A note on the core topology, Annales Math. Silesianae, 5(1991), 28-36.
• [10] Pawlak R.J., The almost continuity of a function of two variables with respect to its sections and core-topology, Atti Sem. Mat. Fis. Univ. Modena, XLVI (1998), 457-468.
• [11] Wagner-Bojakowska E., Wilczyński W., Approximate core topologies. Real Analysis Exchange, 20(l)(1994/95), 192-203.
• [12] Wagner-Bojakowska E., Wilczyński W., Approximate core-a.e. topology, Zeszyty Naukowe Politechniki Łódzkiej Nr 719 - Matematyka, 27(1995), 129-138.