Equivalence of certain free topological groups

Jan Baars

Commentationes Mathematicae Universitatis Carolinae (1992)

  • Volume: 33, Issue: 1, page 125-130
  • ISSN: 0010-2628

Abstract

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In this paper we give a complete isomorphical classification of free topological groups F M ( 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 F M ( X ) and F M ( Y ) are isomorphic if and only if C p ( X ) and C p ( Y ) are linearly homeomorphic.

How to cite

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Baars, Jan. "Equivalence of certain free topological groups." Commentationes Mathematicae Universitatis Carolinae 33.1 (1992): 125-130. <http://eudml.org/doc/247396>.

@article{Baars1992,
abstract = {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.},
author = {Baars, Jan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {free topological groups; function spaces},
language = {eng},
number = {1},
pages = {125-130},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Equivalence of certain free topological groups},
url = {http://eudml.org/doc/247396},
volume = {33},
year = {1992},
}

TY - JOUR
AU - Baars, Jan
TI - Equivalence of certain free topological groups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1992
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 33
IS - 1
SP - 125
EP - 130
AB - 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.
LA - eng
KW - free topological groups; function spaces
UR - http://eudml.org/doc/247396
ER -

References

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  1. Arhangel'skiĭ A.V., A survey of C p -theory, Questions and Answers in General Topology 5 (1987) 1-109. MR0909494
  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. (1988) Zbl0684.54011MR0972840
  3. Engelking R., On closed images of the space of irrationals, Proc. Amer. Math. Soc. 21 (1969), 583-586. (1969) Zbl0177.25501MR0239571
  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). (1962) MR0025474
  5. Graev M.I., Teorija topologičeskih grupp I, Uspehi Math. Nauk 5 (1950), 3-56. (1950) MR0036245
  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). (1962) MR0012301
  7. Okunev O.G., A method for constructing examples of M -equivalent spaces, Top. and its Appl. 36 (1990), 157-171. (1990) Zbl0707.54007MR1068167
  8. Pavlovskiĭ D., On spaces of continuous functions, Soviet Math. Dokl. 22 (1980), 34-37. (1980) 

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