#### Glasnik Matematicki, Vol. 34, No.2 (1999), 263-265.

### A NECESSARY AND SUFFICIENT CONDITION FOR A
SPACE TO BE INFRABARRELLED OR POLYNOMIALLY INFRABARRELLED

### Miguel Caldas Cueva and Dinamerico P. Pombo Jr.

Instituto de Matematica, Universidade Federal Fluminese,
Rua Mario Santos Braga, 24020-140 Niteroi-RJ, Brasil

*e-mail:* `gmamccs@vm.uff.br`

*e-mail:* `marifer@domain.com.br`

**Abstract.** A locally convex space *E* is
infrabarrelled (resp. polynomially infrabarrelled) if and only if,
for every Banach space *F* (resp. for every positive integer
*m* and for every Banach space *F*), the space of all
continous linear mappings from *E* into *F*
(resp. the space of all continuous *m*-homogeous polynomials
form *E* into *F*) is quasi-complete for the topology
of bounded convergence.

**1991 Mathematics Subject Classification.**
46E40.

**Key words and phrases.** Locally convex spaces, continuous
*m*-homogeneous polynomials, topology of bounded convergence,
equicontinuous sets.

**Full text (PDF)** (free access)

*Glasnik Matematicki* Home Page