Results 11 to 20 of about 337 (43)
Compact and extremally disconnected spaces
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 20, Page 1047-1056, 2004., 2004 Viglino defined a Hausdorff topological space to be C‐compact if each closed subset of the space is an H‐set in the sense of Veličko. In this paper, we study the class of Hausdorff spaces characterized by the property that each closed subset is an S‐set in the sense of Dickman and Krystock. Such spaces are called C‐s‐compact.
Bhamini M. P. Nayar
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On unified theory for continuities
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 5, Page 291-301, 2002., 2002 The purpose of this study is to give a unified theory for some weak and strong continuous functions using operations.
Mahide Küçük, Yalçin Küçük
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Fuzzy properties in fuzzy convergence spaces
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 12, Page 737-748, 2002., 2002 Based on the concept of limit of prefilters and residual implication, several notions in fuzzy topology are fuzzyfied in the sense that, for each notion, the degree to which it is fulfilled is considered. We establish therefore theories of degrees of compactness and relative compactness, of closedness, and of continuity.
Gunther Jäger
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Quantification of topological concepts using ideals
International Journal of Mathematics and Mathematical Sciences, Volume 26, Issue 9, Page 561-579, 2001., 2001 We introduce certain ideals of real‐valued functions as a natural generalization of filters. We show that these ideals establish a canonical framework for the quantification of topological concepts, such as closedness, adherence, and compactness, in the setting of approach spaces.
Robert Lowen, Bart Windels
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On S‐cluster sets and S‐closed spaces
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 9, Page 597-603, 2000., 2000 A new type of cluster sets, called S‐cluster sets, of functions and multifunctions between topological spaces is introduced, thereby providing a new technique for studying S‐closed spaces. The deliberation includes an explicit expression of S‐cluster set of a function.
M. N. Mukherjee, Atasi Debray
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International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 3, Page 203-212, 2000., 2000 We will continue the study of p‐closed spaces. This class of spaces is strictly placed between the class of strongly compact spaces and the class of quasi‐H‐closed spaces. We will provide new characterizations of p‐closed spaces and investigate their relationships with some other classes of topological spaces.
Julian Dontchev +2 more
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ℵ1‐directed inverse systems of continuous images of arcs
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 2, Page 109-119, 2000., 2000 The main purpose of this paper is to prove that if X = {Xa, pab, A} is a usual ℵ1‐directed inverse system of continuous images of arcs with monotone bonding mappings, then X = limX is a continuous image of an arc (Theorem 2.4). Some applications of this statement are also given.
Ivan Lončar
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A unified theory for weak separation properties
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 11, Page 765-772, 2000., 2000 We devise a framework which leads to the formulation of a unified theory of normality (regularity), semi‐normality (semi‐regularity), s‐normality (s‐regularity), feebly‐normality (feebly‐regularity), pre‐normality (pre‐regularity), and others. Certain aspects of theory are given by unified proof.
Mahide Küçük, İdris Zorlutuna
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Paracompactness with respect to an ideal
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 3, Page 433-442, 1997., 1995 An ideal on a set X is a nonempty collection of subsets of X closed under the operations of subset and finite union. Given a topological space X and an ideal ℐ of subsets of X, X is defined to be ℐ‐paracompact if every open cover of the space admits a locally finite open refinement which is a cover for all of X except for a set in ℐ.
T. R. Hamlett +2 more
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Application on local discrete expansion
International Journal of Mathematics and Mathematical Sciences, Volume 19, Issue 4, Page 747-750, 1996., 1995 The process of changing a topology by some types of its local discrete expansion preserves s‐closeness, S‐closeness, semi‐compactness, semi‐Ti, semi‐Ri, i ∈ {0, 1, 2}, and extremely disconnectness. Via some other forms of such above replacements one can have topologies which satisfy separation axioms the original topology does not have.
M. E. Abd El-Monsef +2 more
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