Filter space monads, regularity, completions

1974 ◽  
pp. 591-637 ◽  
Author(s):  
Oswald Wyler
Keyword(s):  
Filter Space

scholarly journals A better framework for first countable spaces

2003 ◽  
Vol 4 (2) ◽  
pp. 289
Author(s):  
Gerhard Preuss
Keyword(s):  
Topological Space ◽  
Uniform Space ◽  
Topological Spaces ◽  
Convergence Space ◽  
Convergence Spaces ◽  
Natural Function ◽  
Topological Construct ◽  
Countable Space ◽  
Filter Space ◽  
First Countable Space

<p>In the realm of semiuniform convergence spaces first countability is divisible and leads to a well-behaved topological construct with natural function spaces and one-point extensions such that countable products of quotients are quotients. Every semiuniform convergence space (e.g. symmetric topological space, uniform space, filter space, etc.) has an underlying first countable space. Several applications of first countability in a broader context than the usual one of topological spaces are studied.</p>

scholarly journals Cauchy action on filter spaces

2019 ◽  
Vol 20 (1) ◽  
pp. 177
Author(s):  
N. Rath
Keyword(s):  
Group Action ◽  
Close Link ◽  
Continuous Action ◽  
Filter Space

<p>A Cauchy group (G,D,·) has a Cauchy-action on a filter space (X,C), if it acts in a compatible manner. A new filter-based method is proposed in this paper for the notion of group-action, from which the properties of this action such as transitiveness and its compatibility with various modifications of the G-space (X,C) are determined. There is a close link between the Cauchy action and the induced continuous action on the underlying G-space, which is explored here. In addition, a possible extension of a Cauchy-action to the completion of the underlying G-space is discussed. These new results confirm and generalize some of the properties of group action in a topological context.</p>

scholarly journals Topology on grill-filter space and continuity

2013 ◽  
Vol 31 (2) ◽  
pp. 219 ◽  
Author(s):  
Shyamapada Modak
Keyword(s):  
Generalized Continuity ◽  
Filter Space

This paper will discuss about a new topology, obtained from a grill and a filter on the same set. The Characterizations and open base of the new topology are also aim of this paper. The generalized continuity is also a part of this paper.

A study of local base and adherent point by Double sets in D-Topology

2017 ◽  
Vol 8 (1) ◽  
pp. 24
Author(s):  
Raja Rajeswari ◽  
K. Suguna Devi ◽  
N. Durga Devi
Keyword(s):  
Filter Space ◽  
Local Base

In this paper, we  introduce the  study of D-local base for the D-filter neighbourhood of any D-point  of a double set. The conditions for convergence  of the local base for the D-filter space is derived. The D-adherent points for the D-filter space is defined and also a study of convergence via D-adherent points is carried out.

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