The Redfield topology on some groups of continuous functions.
- Autores: Nadal Batle Nicolau, Josep Grané Manlleu
- Localización: Stochastica: revista de matemática pura y aplicada, ISSN 0210-7821, Vol. 2, Nº. 3, 1977, págs. 23-35
- Idioma: inglés
- Títulos paralelos:
- La topología de Redfield sobre algunos grupos de funciones continuas.
- Enlaces
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Resumen
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.
