Detaching Maps Between Spaces of Continuous Functions
| Autor: | E. BECKENSTEIN, L. NARICI |
|---|---|
| Jazyk: | English<br />French<br />Italian |
| Rok vydání: | 1995 |
| Předmět: | |
| Zdroj: | Rendiconti di Matematica e delle Sue Applicazioni, Vol 15, Iss 4, Pp 607-620 (1995) |
| Druh dokumentu: | article |
| ISSN: | 1120-7183 2532-3350 |
| Popis: | Let C(S) and C(T) denote the spaces of real or complex-valued con- tinuous functions on the Tihonov spaces S and T,respectively. An additive operator H:C(T) -C(S)isseparatingif,forI,r€C(T),Iz=0÷ HxHx=0. In[3]it isshownthatifHisabiseparatingmap(bothHandH-1are separating then the realcompactifications ofS and T are homeomorphic. If H is linear and S and T are realcompact then H is continuous [4]. We investigate weaker conditions on a separating map H than biseparating which imply that H is continuous. For instance, it is shown in theorem 4.2 that if S and UT are locally compact, S connected, H injective and "detaching", then H is a "weighted homomorphism"; such a map is continuous ifT is realcompact. |
| Databáze: | Directory of Open Access Journals |
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