1. Some Identities for a Family of Fibonacci and Lucas Numbers

    Engin Özkan1, Ali Aydoğdu2 and İpek Altun3

    1. Department of Mathematics, Erzincan University, 24100, Erzincan, Turkey.

    2. Department of Mathematics, BeykentUniversity, 34485, İstanbul, Turkey.

    3. Department of Mathematics, Erzincan University, 24100, Erzincan, Turkey.

    Abstract: In this work, we prove some properties of a family of Fibonacci numbers and a family of Lucas numbers. Also,we give some identities between the family of Fibonacci numbers and family of Lucas numbers.

    Keywords: Fibonacci Numbers, Generalized Fibonacci Numbers, Lucas Numbers.

    Pages: 295 – 303 | Full PDF Paper

  2. Fan-Gottesman Compactification and Completeness

    Ceren Sultan ELMALI1 and Tamer UĞUR2

    1. Department of Mathematics, Faculty of Science, Erzurum Technical University, 25100 Erzurum-Turkey.

    2. Department of Mathematics, Faculty of Science, Atatürk University, 25240 Erzurum-Turkey.

    Abstract: It is investigated that Fan-Gottesman compactification of (X, d) is homeomorphic to the completion of (X, dφ) totally bounded metric space. As application, we construct Fan-Gottesman compactification of (Rn, dE), where dE is the euclidean metric and n ≥ 2 and show that Fan-Gottesman compactification of (Rn, dE) is homeomorphic to its completion.

    Keywords: Fan-Gottesman compactification, completion.

    Pages: 304 – 310 | Full PDF Paper