• The Pure and Applied Mathematics
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• v.7 no.2
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• pp.71-78
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• 2000

Any Hausdoroff space on a set which has at least two points a regular closed Boolean algebra different from the indiscrete regular closed Boolean algebra as indiscrete space. The Sierpinski space and the space with finite complement topology on any infinite set etc. do the same. However, there is $T_{0}$ space which does the same with Hausdorpff space as above. The regular closed Boolean algebra in a topological space is isomorphic to that algebra in the space with its open extension topology.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1299-1307
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• 2023

In this paper, we attempt to study several topological properties for the function space H(X), space of self-homeomorphisms on a metric space endowed with the regular topology. We investigate its metrizability and countability and prove their coincidence at X compact. Furthermore, we prove that the space H(X) endowed with the regular topology is a topological group when X is a metric, almost P-space. Moreover, we prove that the homeomorphism spaces of increasing and decreasing functions on ℝ under regular topology are open subspaces of H(ℝ) and are homeomorphic.

• East Asian mathematical journal
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• v.17 no.1
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• pp.1-17
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• 2001

In this paper, fuzzy D-continuous function is defined. Some basic properties of this continuity are summarized; and sufficient conditions on domain and/or ranges implying fuzzy D-continuity of fuzzy D-continuous functions are given. Also fuzzy D-regular space is defined and by using fuzzy D-continuity, the condition which is equivalent to fuzzy D-regular space, is given.

• Journal of the Korean Institute of Intelligent Systems
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• v.12 no.1
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• pp.85-89
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• 2002

In this paper, we introduce the notion of fuzzy regular spaces over a base space and investigate some properties of these spaces.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.375-382
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• 2013

In this paper, I introduce the notion of regular convergence space and give some properties of this space. And I give some conditions for the regularity of continuous convergence structure.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.503-515
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• 2015

In this paper the concepts of pairwise fuzzy regular Volterra spaces and pairwise fuzzy weakly regular Volterra spaces are introduced. Several characterizations of pairwise fuzzy regular Volterra spaces and pair-wise fuzzy weakly regular Volterra spaces are investigated.

• Kyungpook Mathematical Journal
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• v.27 no.1
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• pp.27-33
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• 1987

Minimal s-Urysohn and minimal s-regular spaces are studied. An s-Urysohn (respectively, s-regular) space (X, $\mathfrak{T}$) is said to be minimal s-Urysohn (respectively, minimal s-regular) if for no topology $\mathfrak{T}^{\prime}$ on X which is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) is s-Urysohn (respectively s-regular). Several characterizations and other related properties of these classes of spaces have been obtained. The present paper is a study of minimal P-spaces where P refers to the property of being an s-Urysohn space or an s-regular space. A P-space (X, $\mathfrak{T}$) is said to be minimal P if for no topology $\mathfrak{T}^{\prime}$ on X such that $\mathfrak{T}^{\prime}$ is strictly weaker than $\mathfrak{T}$, (X, $\mathfrak{T}^{\prime}$) has the property P. A space X is said to be s-Urysohn [2] if for any two distinct points x and y of X there exist semi-open set U and V containing x and y respectively such that $clU{\bigcap}clV={\phi}$, where clU denotes the closure of U. A space X is said to be s-regular [6] if for any point x and a closed set F not containing x there exist disjoint semi-open sets U and V such that $x{\in}U$ and $F{\subseteq}V$. Throughout the paper the spaces are assumed to be Hausdorff.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.1
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• pp.45-57
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• 2011

We study the stochastic integral of an operator valued process against with a Banach space valued regular process. We establish the existence and uniqueness of solution of the stochastic differential equation for a Banach space valued regular process under the certain conditions. As an application of it, we study a noncommutative stochastic differential equation.

• Honam Mathematical Journal
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• v.31 no.3
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• pp.279-292
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• 2009

As a survey-type article, the paper reviews some results on a regular covering space in digital covering theory. The recent paper [10](see also [12]) established the notion of regular covering space in digital covering theory and studied its various properties. Besides, the papers [14, 16] developed a discrete Deck's transformation group of a digital covering. In this paper we study further their properties. By using these properties, we can classify digital covering spaces. Finally, the paper proposes an open problem.

• Journal of Computing Science and Engineering
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• v.8 no.2
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• pp.78-86
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• 2014

Aiming to solve the problems of high memory access and big storage space and long matching time in the regular expression matching of extended finite automaton (XFA), a new regular expression matching algorithm based on high-efficient finite automaton is presented in this paper. The basic idea of the new algorithm is that some extra judging instruments are added at the starting state in order to reduce any unnecessary transition paths as well as to eliminate any unnecessary state transitions. Consequently, the problems of high memory access consumption and big storage space and long matching time during the regular expression matching process of XFA can be efficiently improved. The simulation results convey that our proposed scheme can lower approximately 40% memory access, save about 45% storage space consumption, and reduce about 12% matching time during the same regular expression matching process compared with XFA, but without degrading the matching quality.