The Redfield topology on some groups of continuous functions.

Título inglés	The Redfield topology on some groups of continuous functions.
Título español	La topología de Redfield sobre algunos grupos de funciones continuas.
Autor/es	Batle Nicolau, Nadal ; Grané Manlleu, Josep
Organización	Inst. Mat. Apl. Univ. Politéc. Barcelona, Barcelona, España
Revista	0210-7821
Publicación	1977, 2 (3): 23-35, 6 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	The Redfield topology on the space of real-valued continuous functions on a topological space is studied (we call it R-topology for short). The R-neighbourhoods are described relating them to the connectedness for the carriers. The main results are: If the space is totally disconnected without isolated points, the R-topology is not discrete. Under suitable conditions on the space, R-convergence implies pointwise or uniform convergence. Under some restrictions, R-convergence for a net implies that the net be eventually pointwise constant. For better behaving spaces we show that the only R-convergent sequences are the almost constant ones. In spite of corollary 5.2 of [1] we give a direct proof for the Redfield topology to be not discrete. We finally remark that for some spaces the R-topology is not first countable.
Clasificación UNESCO	121005
Palabras clave español	Topología general ; Espacios topológicos ; Espacios de funciones continuas
Código MathReviews	MR0562429
Código Z-Math	Zbl 0422.06011
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