Productively sequential spaces

2018 ◽  
Vol 68 (3) ◽  
pp. 667-676 ◽  
Author(s):  
Szymon Dolecki ◽  
Frédéric Mynard
Keyword(s):  
Sequential Space ◽  
Regular Topology ◽  
Sequential Spaces

Abstract We characterize productively sequential spaces, that is, spaces whose product with every strongly sequential space is sequential, equivalently strongly sequential. It turns out that a regular topology is productively sequential if and only if it is sequential and bi-quasi-k.

scholarly journals Minimal sequential Hausdorff spaces

2004 ◽  
Vol 2004 (22) ◽  
pp. 1169-1177
Author(s):  
Bhamini M. P. Nayar
Keyword(s):  
Hausdorff Spaces ◽  
Sequential Space ◽  
Compact Spaces ◽  
Countably Compact ◽  
Countably Compact Spaces ◽  
Sequential Spaces ◽  
By Products

A sequential space(X,T)is called minimal sequential if no sequential topology onXis strictly weaker thanT. This paper begins the study of minimal sequential Hausdorff spaces. Characterizations of minimal sequential Hausdorff spaces are obtained using filter bases, sequences, and functions satisfying certain graph conditions. Relationships between this class of spaces and other classes of spaces, for example, minimal Hausdorff spaces, countably compact spaces, H-closed spaces, SQ-closed spaces, and subspaces of minimal sequential spaces, are investigated. While the property of being sequential is not (in general) preserved by products, some information is provided on the question of when the product of minimal sequential spaces is minimal sequential.

scholarly journals Further aspects of I K-convergence in topological spaces

2021 ◽  
Vol 22 (2) ◽  
pp. 355
Author(s):  
Ankur Sharmah ◽  
Debajit Hazarika
Keyword(s):  
Topological Space ◽  
Topological Spaces ◽  
Sequential Space ◽  
Ideal Convergence ◽  
Limit Points ◽  
Sequential Spaces ◽  
Cluster Points

In this paper, we obtain some results on the relationships between different ideal convergence modes namely, I K, I K∗ , I, K, I ∪ K and (I ∪K) ∗ . We introduce a topological space namely I K-sequential space and show that the class of I K-sequential spaces contain the sequential spaces. Further I K-notions of cluster points and limit points of a function are also introduced here. For a given sequence in a topological space X, we characterize the set of I K-cluster points of the sequence as closed subsets of X.

scholarly journals Some classes of sequential spaces

1993 ◽  
Vol 47 (3) ◽  
pp. 377-384
Author(s):  
Sergey A. Svetlichny
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Sequential Space ◽  
Sequential Spaces

By means of defined concepts all metric spaces of given weight or cardinality and their quotients are characterised. An example of a sequential space having weight w1 which is not a quotient of any metric space of weight w1 is provided. The well-known classes of sequential spaces are also obtained as images of metric spaces by particular kinds of maps.

scholarly journals An Ascoli theorem for sequential spaces

2001 ◽  
Vol 26 (5) ◽  
pp. 303-315 ◽  
Author(s):  
Gert Sonck
Keyword(s):  
Function Space ◽  
Uniform Space ◽  
Continuous Functions ◽  
Space Structure ◽  
Sequential Space ◽  
Continuous Convergence ◽  
Natural Function ◽  
Sequential Spaces

Ascoli theorems characterize “precompact” subsets of the set of morphisms between two objects of a category in terms of “equicontinuity” and “pointwise precompactness,” with appropriate definitions of precompactness and equicontinuity in the studied category. An Ascoli theorem is presented for sets of continuous functions from a sequential space to a uniform space. In our development we make extensive use of the natural function space structure for sequential spaces induced by continuous convergence and define appropriate concepts of equicontinuity for sequential spaces. We apply our theorem in the context ofC*-algebras.

scholarly journals On countable choice and sequential spaces

2008 ◽  
Vol 54 (2) ◽  
pp. 145-152 ◽  
Author(s):  
Gonçalo Gutierres
Keyword(s):  
Sequential Spaces

scholarly journals Separation in sequential spaces under PMEA

1990 ◽  
Vol 134 (2) ◽  
pp. 117-123
Author(s):  
Peg Daniels
Keyword(s):  
Sequential Spaces

Two R-Closed Spaces

1972 ◽  
Vol 24 (2) ◽  
pp. 286-292 ◽  
Author(s):  
R. M. Stephenson
Keyword(s):  
Closed Subset ◽  
Fundamental System ◽  
Regular Space ◽  
Closed Space ◽  
Regular Topology ◽  
Regular Closed

Throughout this paper all hypothesized spaces are T1. A regular space is called R-closed[11](regular-closed [7] or, equivalently, regular-complete [2]) provided that it is a closed subset of any regular space in which it can be embedded. A regular space (X, ℐ) is called minimal regular [2; 4] if there exists no regular topology on X which is strictly weaker than J. We shall call a regular space X strongly minimal regular provided that each point x ∈ X has a fundamental system of neighbourhoods such that for every V ∈ , X\V is an R-closed space.In §2 we note that a strongly minimal regular space is minimal regular, but we do not know if the converse holds. M. P. Berri and R. H. Sorgenfrey [4] proved that a minimal regular space is R-closed, and Horst Herrlich [7] gave an example of an R-closed space that is not minimal regular.

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