• 제목/요약/키워드: compactness conditions

검색결과 62건 처리시간 0.019초

Variants of Compactness in Pointfree Topology

  • Banaschewski, Bernhard;Hong, Sung Sa
    • Kyungpook Mathematical Journal
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    • 제45권4호
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    • pp.455-470
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    • 2005
  • This paper introduces compactness notions for frames which are expressed in terms of the convergence of suitably specified general filters. It establishes several preservation properties for them as well as their coreflectiveness in the setting of regular frames. Further, it shows that supercompact, compact, and $Lindel{\ddot{o}}f$ frames can be described by compactness conditions of the present form so that various familiar facts become consequences of these general results. In addition, the Prime Ideal Theorem and the Axiom of Countable Choice are proved to be equivalent to certain conditions connected with the kind of compactness considered here.

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ON SPACES IN WHICH THE THREE MAIN KINDS OF COMPACTNESS ARE EQUIVALENT

  • Hong, Woo-Chorl
    • 대한수학회논문집
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    • 제25권3호
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    • pp.477-484
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    • 2010
  • In this paper, we introduce a new property (*) of a topological space and prove that if X satisfies one of the following conditions (1) and (2), then compactness, countable compactness and sequential compactness are equivalent in X; (1) Each countably compact subspace of X with (*) is a sequential or AP space. (2) X is a sequential or AP space with (*).

FROM STRONG CONTINUITY TO WEAK CONTINUITY

  • Kim, Jae-Woon
    • 충청수학회지
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    • 제14권1호
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    • pp.29-40
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    • 2001
  • In this note, we get the conditions such that strong continuity ${\Rightarrow}$ weak continuity plus interiority condition( wc+ic), and continuity ${\Rightarrow}$ wc+ic are true. And we investigate some equivalent conditions with weak continuity, some properties of weak continuity. And we show that almost compactness is preserved by weakly continuous function, and we improve some known results with respect to strong continuity.

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SEVEN GENERALIZED TYPES OF SOFT SEMI-COMPACT SPACES

  • Al-shami, Tareq Mohammed;El-Shafei, Mohammed E.;Abo-Elhamayel, Mohammed
    • Korean Journal of Mathematics
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    • 제27권3호
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    • pp.661-690
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    • 2019
  • The soft compactness notion via soft topological spaces was first studied in [10,29]. In this work, soft semi-open sets are utilized to initiate seven new kinds of generalized soft semi-compactness, namely soft semi-$Lindel{\ddot{o}}fness$, almost (approximately, mildly) soft semi-compactness and almost (approximately, mildly) soft semi-$Lindel{\ddot{o}}fness$. The relationships among them are shown with the help of illustrative examples and the equivalent conditions of each one of them are investigated. Also, the behavior of these spaces under soft semi-irresolute maps are investigated. Furthermore, the enough conditions for the equivalence among the four sorts of soft semi-compact spaces and for the equivalence among the four sorts of soft semi-$Lindel{\ddot{o}}f$ spaces are explored. The relationships between enriched soft topological spaces and the initiated spaces are discussed in different cases. Finally, some properties which connect some of these spaces with some soft topological notions such as soft semi-connectedness, soft semi $T_2$-spaces and soft subspaces are obtained.

ON A CLASS OF NONCOOPERATIVE FOURTH-ORDER ELLIPTIC SYSTEMS WITH NONLOCAL TERMS AND CRITICAL GROWTH

  • Chung, Nguyen Thanh
    • 대한수학회지
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    • 제56권5호
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    • pp.1419-1439
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    • 2019
  • In this paper, we consider a class of noncooperative fourth-order elliptic systems involving nonlocal terms and critical growth in a bounded domain. With the help of Limit Index Theory due to Li [32] combined with the concentration compactness principle, we establish the existence of infinitely many solutions for the problem under the suitable conditions on the nonlinearity. Our results significantly complement and improve some recent results on the existence of solutions for fourth-order elliptic equations and Kirchhoff type problems with critical growth.

POSITIVE SOLUTION AND GROUND STATE SOLUTION FOR A KIRCHHOFF TYPE EQUATION WITH CRITICAL GROWTH

  • Chen, Caixia;Qian, Aixia
    • 대한수학회보
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    • 제59권4호
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    • pp.961-977
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    • 2022
  • In this paper, we consider the following Kirchhoff type equation on the whole space $$\{-(a+b{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{R}}^3}}}\;{\mid}{\nabla}u{\mid}^2dx){\Delta}u=u^5+{\lambda}k(x)g(u),\;x{\in}{\mathbb{R}}^3,\\u{\in}{\mathcal{D}}^{1,2}({\mathbb{R}}^3),$$ where λ > 0 is a real number and k, g satisfy some conditions. We mainly investigate the existence of ground state solution via variational method and concentration-compactness principle.

밀집형 재생증발식 냉방기의 냉각 성능 분석 (Analysis of Cooling Performance of a Compact Regenerative Evaporative Cooler)

  • 박민희;문승재;이대영
    • 설비공학논문집
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    • 제28권8호
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    • pp.316-324
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    • 2016
  • This study investigated a compact regenerative evaporative cooler (REC). To achieve practical applications of an REC, it is very important to consider the compactness as well as the cooling performance. Therefore, a prototype of the REC was designed and fabricated to improve the compactness by reducing the length through the insertion of fins in both the dry and wet channels. The REC prototype was tested in terms of performance evaluation under various operating conditions. An analytical model was also developed to analyze the effects of the axial conduction through the solid body of the REC, the wetness of the surface in the wet channel, and the thermal capacity of the evaporation water flow. The model was validated by comparing the results of a simulation with experimental data. The numerical simulation was based on the model to analyze the performance of the REC and to suggest methods to improve the cooling performance of the REC. Finally, the performance of the present REC was compared to that obtained in previous experimental studies. The results showed that the REC prototype in the present study is the most compact and achieves the highest cooling performance.

GLOBAL ATTRACTOR OF THE WEAKLY DAMPED WAVE EQUATION WITH NONLINEAR BOUNDARY CONDITIONS

  • Zhu, Chaosheng
    • 대한수학회논문집
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    • 제27권1호
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    • pp.97-106
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    • 2012
  • In this paper, the main purpose is to study existence of the global attractors for the weakly damped wave equation with nonlinear boundary conditions. To this end, we first show that the existence o a bounded absorbing set by the perturbed energy method. Secondly, we utilize the decomposition of the solution operator to verify the asymptotic compactness.

HYBRID FIXED POINT THEORY AND EXISTENCE OF EXTREMAL SOLUTIONS FOR PERTURBED NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

  • Dhage, Bapurao C.
    • 대한수학회보
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    • 제44권2호
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    • pp.315-330
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    • 2007
  • In this paper, some hybrid fixed point theorems are proved which are further applied to first and second order neutral functional differential equations for proving the existence results for the extremal solutions under the mixed Lipschitz, compactness and monotonic conditions.