# The Redfield topology on some groups of continuous functions.

Nadal Batle Nicolau; Josep Grané Manlleu

Stochastica (1977)

- Volume: 2, Issue: 3, page 23-35
- ISSN: 0210-7821

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topBatle 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 -

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