Geodesic
Equivalence of certain free topological groups
Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 125-130 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

In this paper we give a complete isomorphical classification of free topological groups $FM(X)$ of locally compact zero-dimensional separable metric spaces $X$. From this classification we obtain for locally compact zero-dimensional separable metric spaces $X$ and $Y$ that the free topological groups $FM (X)$ and $FM(Y)$ are isomorphic if and only if $C_p(X)$ and $C_p(Y)$ are linearly homeomorphic.
In this paper we give a complete isomorphical classification of free topological groups $FM(X)$ of locally compact zero-dimensional separable metric spaces $X$. From this classification we obtain for locally compact zero-dimensional separable metric spaces $X$ and $Y$ that the free topological groups $FM (X)$ and $FM(Y)$ are isomorphic if and only if $C_p(X)$ and $C_p(Y)$ are linearly homeomorphic.
Classification : 22A05, 54C35, 54H11
Keywords: free topological groups; function spaces 
@article{CMUC_1992_33_1_a14,
     author = {Baars, Jan},
     title = {Equivalence of certain free topological groups},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {125--130},
     year = {1992},
     volume = {33},
     number = {1},
     mrnumber = {1173754},
     zbl = {0759.54022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1992_33_1_a14/}
}
TY  - JOUR
AU  - Baars, Jan
TI  - Equivalence of certain free topological groups
JO  - Commentationes Mathematicae Universitatis Carolinae
PY  - 1992
SP  - 125
EP  - 130
VL  - 33
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/CMUC_1992_33_1_a14/
LA  - en
ID  - CMUC_1992_33_1_a14
ER  - 
%0 Journal Article
%A Baars, Jan
%T Equivalence of certain free topological groups
%J Commentationes Mathematicae Universitatis Carolinae
%D 1992
%P 125-130
%V 33
%N 1
%U http://geodesic.mathdoc.fr/item/CMUC_1992_33_1_a14/
%G en
%F CMUC_1992_33_1_a14
Baars, Jan. Equivalence of certain free topological groups. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) no. 1, pp. 125-130. http://geodesic.mathdoc.fr/item/CMUC_1992_33_1_a14/

[1] Arhangel'skiĭ A.V.: A survey of $C_p$-theory. Questions and Answers in General Topology 5 (1987) 1-109. | MR

[2] Baars J., de Groot J.: An isomorphical classification of function spaces of zero-dimensional locally compact separable metric spaces. Comment. Math. Univ. Carolinae 29 (1988), 577-595. | MR | Zbl

[3] Engelking R.: On closed images of the space of irrationals. Proc. Amer. Math. Soc. 21 (1969), 583-586. | MR | Zbl

[4] Graev M.I.: Free topological groups. Am. Math. Soc. Transl. (1) 8 (1962), 305-364 (translation from {Svobodnye topologičeskie gruppy}, Izvestiya Akad. Nauk SSSR, Ser. Mat. 12 (1948) 279-324). | MR

[5] Graev M.I.: Teorija topologičeskih grupp I. Uspehi Math. Nauk 5 (1950), 3-56. | MR

[6] Markov A.A.: On free topological groups. Am. Math. Soc. Transl. (1) 8 (1962), 195-272 (translation from {O svobodnyh topologičeskih gruppah}, Izvestiya Akad. Nauk SSSR, Ser. Mat. 9 (1945) 3-64). | MR

[7] Okunev O.G.: A method for constructing examples of $M$-equivalent spaces. Top. and its Appl. 36 (1990), 157-171. | MR | Zbl

[8] Pavlovskiĭ D.: On spaces of continuous functions. Soviet Math. Dokl. 22 (1980), 34-37.