| Title:
|
Equivalence of certain free topological groups (English) |
| Author:
|
Baars, Jan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
125-130 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
free topological groups |
| Keyword:
|
function spaces |
| MSC:
|
22A05 |
| MSC:
|
54C35 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 0759.54022 |
| idMR:
|
MR1173754 |
| . |
| Date available:
|
2009-01-08T17:54:07Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118478 |
| . |
| Reference:
|
[1] Arhangel'skiĭ A.V.: A survey of $C_p$-theory.Questions and Answers in General Topology 5 (1987) 1-109. MR 0909494 |
| Reference:
|
[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. Zbl 0684.54011, MR 0972840 |
| Reference:
|
[3] Engelking R.: On closed images of the space of irrationals.Proc. Amer. Math. Soc. 21 (1969), 583-586. Zbl 0177.25501, MR 0239571 |
| Reference:
|
[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 0025474 |
| Reference:
|
[5] Graev M.I.: Teorija topologičeskih grupp I.Uspehi Math. Nauk 5 (1950), 3-56. MR 0036245 |
| Reference:
|
[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 0012301 |
| Reference:
|
[7] Okunev O.G.: A method for constructing examples of $M$-equivalent spaces.Top. and its Appl. 36 (1990), 157-171. Zbl 0707.54007, MR 1068167 |
| Reference:
|
[8] Pavlovskiĭ D.: On spaces of continuous functions.Soviet Math. Dokl. 22 (1980), 34-37. |
| . |
