• Journal of the Korean Mathematical Society
• /
• v.49 no.3
• /
• pp.449-473
• /
• 2012

In the present paper, we study the relationship between continuous order-representability and the fulfillment of the usual covering properties on topological spaces. We also consider the case of some algebraic structures providing an application of our results to the social choice theory context.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.1
• /
• pp.53-69
• /
• 2013

Topology may described a pattern of existence of elements of a given set X. The family ${\tau}(X)$ of all topologies given on a set X form a complete lattice. We will give some topologies on this lattice ${\tau}(X)$ using a topology on X and regard ${\tau}(X)$ a topological space. A topology ${\tau}$ on X can be regarded a map from X to ${\tau}(X)$ naturally. Such a map will be called topology field. Similarly we can also define pe-topology field. If X is a topological flow group with acting group T, then naturally we can get a another topological flow ${\tau}(X)$ with same acting group T. If the topological flow X is minimal, we can prove ${\tau}(X)$ is also minimal. The disjoint unions of the topological spaces can describe some topological systems (topological organisms). Here we will give a definition of topological organism. Our purpose of this study is to describe some properties concerning patterns of relationship between topology fields and topological organisms.

• Communications of the Korean Mathematical Society
• /
• v.25 no.3
• /
• pp.335-342
• /
• 2010

The structure of fuzzy topological spaces based on WFI-algebras is considered. The notions of WFI-fuzzy topological spaces and WFI-fuzzy continuous mappings are introduced, and several properties are investigated. A relation between WFI-homomorphism and WFI-fuzzy continuous mapping is given.

• Journal of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.841-857
• /
• 2009

In this paper, we give and study the notion of computer topological function space between computer topological spaces with $k_i$ adjacency, i $\in$ {0, 1}. Using this notion, we study various properties of topologies of a computer topological function space.

• Elastomers and Composites
• /
• v.37 no.4
• /
• pp.234-243
• /
• 2002

A general scheme of a rubber structure is proposed. Using the thermomechanical method(TMA), some changes in the molecular and topological structures for uncured and cured, and unfilled and filled rubbers during processing are shown. In our investigations as region it is understood a complex structure, which is expressed at the thermomechanical curve(TMC) as a zone differed from others in thermal expansion properties. This zone is between the noticed temperatures of relaxation transitions, usually on the level like those determined by DMTA at 1Hz. These regions, which shares, are not stable, and differ in molecular-weight distribution(MWD) of chain fragments between the junctions. Differences in dynamics of the formation of the molecular and topological structures of a vulcanizate are dependent on the rubber formulation, mixing technology and curing time. Some of characteristics of these regions correlate with mechanical properties of vulcanizates what is shown for NR rubbers containing ENR or CPE as a polymeric additive. It is well known that the state of order influences diffusivity of low-molecular substances into the polymer matrix. Because of this, the two topological amorphous regions should influence the distribution of the ingredients and resulting in rubber compounds' heterogeneity, and related properties of cured rubber. Investigation of this problem is expected to be, in the future, one of the essential factors in determining further improvement of polymeric materials properties by compounding with additives and in reprocessing of rubber scrap.

• Honam Mathematical Journal
• /
• v.34 no.4
• /
• pp.559-570
• /
• 2012

We construct a new definition of a base for ordinary smooth topological spaces and introduce the concept of a neighborhood structure in ordinary smooth topological spaces. Then, we state some of their properties which are generalizations of some results in classical topological spaces.

• Honam Mathematical Journal
• /
• v.32 no.4
• /
• pp.619-624
• /
• 2010

We introduce the notions of bigeneralized topological spaces and quasi generalized open sets, and study some basic properties for the sets. We also introduce the notion of quasi generalized continuity on bigeneralized topological spaces, and investigate characterizations for the continuity.

• Journal of applied mathematics & informatics
• /
• v.10 no.1_2
• /
• pp.361-370
• /
• 2002

We are to present some properties of binary relations on fuzzy topological spares by means of categorical method. The concept of fuzzy topological ordered spaces was introduced by Katsaras[8]. In this paper we study some special categories, i.e, FTQOS, FTPOS, LSCQ, USCQ, SCQ, CQ, NQO, CRQO, associated with fuzzy topological spaces.

• Journal of the Chungcheong Mathematical Society
• /
• v.20 no.1
• /
• pp.31-35
• /
• 2007

In dealing with transformation group, topological approach is very natural. But, it is not sufficient to investigate geometric properties of transformation group and we need geometric method. Frankel-McDuff Conjecture is very interesting in the point that it shows struggling between topological method and geometric method. In this paper, the author suggest generalized Frankel-McDuff conjecture as a topological version of the conjecture and construct a counterexample for the generalized version, and from this we assert that topological method does not work for Frankel-McDuff Conjecture.

• Bulletin of the Korean Chemical Society
• /
• v.25 no.2
• /
• pp.253-259
• /
• 2004

Some new topological indices based on the distance matrix and Randic connectivity (as graph invariants) are proposed. The calculation of these indices is simple and they have good discriminating ability toward alkanes. Incorporating the number of carbon atoms to one of the calculated indices gives a highly correlating topological index (Sh index) which found to correlate with selected physicochemical properties of wide range of alkanes, specially, their boiling points. Most of the investigated properties are well modeled (with $r^2$> 0.99) by the Sh index. Meanwhile, the resulting regressions were compared with the results based on the well-established Randic and newly reported Xu indices and, in most cases, better results were obtained by the Sh index. Moreover, multiple linear regression analysis of the alkane properties via calculated indices gives highly correlating models with low standard errors.