The Redfield topology on some groups of continuous functions.

Batle Nicolau, Nadal, and Grané Manlleu, Josep. "The Redfield topology on some groups of continuous functions.." Stochastica 2.3 (1977): 23-35. <http://eudml.org/doc/38800>.

@article{BatleNicolau1977,
abstract = {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.},
author = {Batle Nicolau, Nadal, Grané Manlleu, Josep},
journal = {Stochastica},
keywords = {Topología general; Espacios topológicos; Espacios de funciones continuas; lattice ordered group; R-topology; R-convergence; uniform convergence},
language = {eng},
number = {3},
pages = {23-35},
title = {The Redfield topology on some groups of continuous functions.},
url = {http://eudml.org/doc/38800},
volume = {2},
year = {1977},
}

TY - JOUR
AU - Batle Nicolau, Nadal
AU - Grané Manlleu, Josep
TI - The Redfield topology on some groups of continuous functions.
JO - Stochastica
PY - 1977
VL - 2
IS - 3
SP - 23
EP - 35
AB - 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.
LA - eng
KW - Topología general; Espacios topológicos; Espacios de funciones continuas; lattice ordered group; R-topology; R-convergence; uniform convergence
UR - http://eudml.org/doc/38800
ER -