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In this article we introduce the concept of $z^circ$-filter on a topological space $X$. We study and investigate the behavior of $z^circ$-filters and compare them  with corresponding ideals, namely, $z^circ$-ideals of $C(X)$,  the ring of real-valued continuous functions on a completely regular Hausdorff space $X$. It is observed that $X$ is a compact space if and only if every $z^circ$-filter ...

‎It is well known that every (real or complex) normed linear space $L$ is isometrically embeddable into $C(X)$ for some compact Hausdorff space $X$‎. ‎Here $X$ is the closed unit ball of $L^*$ (the set of all continuous scalar-valued linear mappings on $L$) endowed with the weak$^*$ topology‎, ‎which is compact by the Banach--Alaoglu theorem‎. ‎We prove that the compact Hausdorff space $X$ can ...

With the rapid growth of information and communication technologies, the attempt for more convenient, safe, and sustainable urban development has been going around the world. The Korean government has launched a R&D project to develop a new software platform that supports the smart city applications such as transportation, anti-disaster, anti-crime, and eco-friendly environment. This paper repo...

In this paper, a Krein-Milman  type theorem in $T_0$ semitopological cone is proved,  in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.

The present paper introduces the notion of the complete fuzzy norm on a linear space. And, some relations between the fuzzy completeness and ordinary completeness on a linear space is considered, moreover a new form of fuzzy compact spaces, namely b-compact spaces and b-closed spaces are introduced. Some characterizations of their properties are obtained.

background: vitrification has proven to be more effective than slow freezing methods to cryopreserve mammalian oocytes. the objectives of this study were to evaluate the effects of vitrification on immature and in vitro matured, denuded and cumulus compact goat oocytes and their subsequent fertilization. methods: oocytes were either cryopreserved as immature cumulus compact (imcc) (n=98 exp 1; ...

let $pounds$ be the category of all locally compact abelian (lca) groups‎. ‎in this paper‎, ‎the groups $g$ in $pounds$ are determined such that every extension $0to xto yto gto 0$ with divisible‎, ‎$sigma-$compact $x$ in $pounds$ splits‎. ‎we also determine the discrete or compactly generated lca groups $h$ such that every pure extension $0to hto yto xto 0$ splits for each divisible group $x$ ...

Whether a city develops toward a more compact or sprawling one may affect many aspects of urban environment, such as public and ecosystem health, greenhouse gas emissions, and quality of life. Using longitudinal data of Chinese cities during 2000-2010, we investigate the relationship between the compactness of urban growth, measured by average population density and several important indicators...