On certain groups of functions
Let C(X,G) denote the group of continuous functions from a topological space X into a topological group G with the pointwise multiplication and the compact-open topology. We show that there is a natural topology on the collection of normal subgroups Δ(X) of C(X,G) of the Mp={f∈C(X,G):f(p)=e} which i...
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Hindawi Limited
1980-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171280000373 |
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doaj-38f9fe8861124e96827274e9a78705f12020-11-24T23:19:54ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251980-01-013349150410.1155/S0161171280000373On certain groups of functionsJ. S. Yang0Department of Mathematics, Computer Science, and Statistics, University of South Carolina, Columbia 29208, South Carolina, USALet C(X,G) denote the group of continuous functions from a topological space X into a topological group G with the pointwise multiplication and the compact-open topology. We show that there is a natural topology on the collection of normal subgroups Δ(X) of C(X,G) of the Mp={f∈C(X,G):f(p)=e} which is analogous to the hull-kernel topology on the commutative Banach algegra C(X) of all continuous real or complex-valued functions on X. We also investigate homomorphisms between groups C(X,G) and C(Y,G).http://dx.doi.org/10.1155/S0161171280000373continuous functionstopological groupcompact-open topologyhull-kernel topologynormal subgroupsS-pairS-topologyBanach algebrastructure space. |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
J. S. Yang |
| spellingShingle |
J. S. Yang On certain groups of functions International Journal of Mathematics and Mathematical Sciences continuous functions topological group compact-open topology hull-kernel topology normal subgroups S-pair S-topology Banach algebra structure space. |
| author_facet |
J. S. Yang |
| author_sort |
J. S. Yang |
| title |
On certain groups of functions |
| title_short |
On certain groups of functions |
| title_full |
On certain groups of functions |
| title_fullStr |
On certain groups of functions |
| title_full_unstemmed |
On certain groups of functions |
| title_sort |
on certain groups of functions |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
1980-01-01 |
| description |
Let C(X,G) denote the group of continuous functions from a topological space X into a topological group G with the pointwise multiplication and the compact-open topology. We show that there is a natural topology on the collection of normal subgroups Δ(X) of C(X,G) of the Mp={f∈C(X,G):f(p)=e} which is analogous to the hull-kernel topology on the commutative Banach algegra C(X) of all continuous real or complex-valued functions on X. We also investigate homomorphisms between groups C(X,G) and C(Y,G). |
| topic |
continuous functions topological group compact-open topology hull-kernel topology normal subgroups S-pair S-topology Banach algebra structure space. |
| url |
http://dx.doi.org/10.1155/S0161171280000373 |
| work_keys_str_mv |
AT jsyang oncertaingroupsoffunctions |
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1725576333504806912 |