Az Eszterházy Károly Tanárképző Főiskola Tudományos Közleményei. 1997. Sectio Mathematicae. (Acta Academiae Paedagogicae Agriensis : Nova series ; Tom. 24)

CERETKOVÁ, S., FULIER, J. and TÓTH J. T., On the certain subsets of the space of metrics

On the certain subsets of the space of metrics 115 (The same function was used in [2], Theorem 5.) It can be easily verified that dß

(x

n,xi) —» oc(n —• oo), hence f(dß

) = Thereby we have 2

car

dW possibilities for choosing of B, we get that card(/

_

1 ({i})) = 2

car

d(

x). 2. For t = 0 it has been proved in [4] (Theorem 1), that card(<71 ({£})) = 2card(X) Le

t í > 0. Let 5 C I is so, that card(£) > 2. Define p

B on X as follows: {

0, for x = y t for x,y E B,x ± y t + 1 otherwise. Then pß E M and g(pn) — t. 3. Let t > 0 and 0 < ( < Then the function Tß defined on X by this way {

0, for x = y t, for x,y E B, x ± y t — ( otherwise, is a metric on X and h(rß) = t. • References [1] R. ENGELKING, General Topology, PWN, Warszawa, 1977 (in russian). [2] T. SALAT, J. TÓTH, L. ZSILINSZKY

, Metric space of metrics defined on a given set, Real Anal. Exch

., 18 No. 1 (1992/93), 225-231. [3] T. SALAT, J. TÓTH, L. ZSILINSZKY

, On structure of the space of metrics defined on a given set, Real Anal. Exch., 19 No. 1 (1993/94), 321-327. [4] R. W. VALLIN, More on the metric space of metrics, Real. Anal. Exch., 21 No. 2. (1995/96), 739-742. UNIVERSITY OF EDUCATION, DEPARTMENT OF MATHEMATICS, FARSKA 19, 949 74 NITRA, SLOVAKIA E-mail: toth@unitra.sk