• 충청수학회지
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• 제22권3호
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• pp.353-358
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• 2009

In [6], the author introduced the concepts of $s\gamma$-open sets and $s\gamma$-continuous functions. In this paper, we introduce the concept of weak $s\gamma$-continuity which is a generalization of $s\gamma$-continuity and weak continuity and investigate characterizations for such functions.

• 대한수학회보
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• 제31권2호
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• pp.187-192
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• 1994

The author extended the small properties of topological semilattices to that of regular semigroups [3]. In this paper, it could be shown that a semigroup S is almost regular if and only if over bar RL = over bar R.cap.L for every right ideal R and every left ideal L of S. Moreover, it has shown that the Bohr compactification of an almost regular semigroup is regular. Throughout, a semigroup will mean a topological semigroup which is a Hausdorff space together with a continuous associative multiplication. For a semigroup S, we denote E(S) by the set of all idempotents of S. An element x of a semigroup S is called regular if and only if x .mem. xSx. A semigroup S is termed regular if every element of S is regular. If x .mem. S is regular, then there exists an element y .mem S such that x xyx and y = yxy (y is called an inverse of x) If y is an inverse of x, then xy and yx are both idempotents but are not always equal. A semigroup S is termed recurrent( or almost pointwise periodic) at x .mem. S if and only if for any open set U about x, there is an integer p > 1 such that x$^{p}$ .mem.U.S is said to be recurrent (or almost periodic) if and only if S is recurrent at every x .mem. S. It is known that if x .mem. S is recurrent and .GAMMA.(x)=over bar {x,x$^{2}$,..,} is compact, then .GAMMA.(x) is a subgroup of S and hence x is a regular element of S.

• 천문학회지
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• 제35권3호
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• pp.131-141
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• 2002

We present Near-IR photometry of the Arches cluster, a young and massive stellar cluster near the Galactic center. We have analyzed the high resolution (FWHM $\~$ 0.2") Hand K' band images in the Galactic Center Demonstration Science Data Set, which were obtained with the Gemini/Hokupa's adaptive optics (AO) system. We present the color-magnitude diagram, the luminosity function and the initial mass function (IMF) of the stars in the Arches cluster in comparison with the HST/NICMOS data. The IMF slope for the range of 1.0 < log (M/M$\bigodot$) < 2.1 is estimated to be ${\Gamma} = -0.79 {\pm} 0.16$, in good agreements with the earlier result based on the HST/NICMOS data [Figer et al. 1999, ApJ, 525, 750]. These results strengthen the evidence that the IMF of the bright. stars close to the Galactic center is much flatter than that for the solar neighborhood. This is also consistent with a recent finding that the IMFs of the bright stars in young clusters in M33 get flatter as the galactocentric distance decreases [Lee et al. 2001, astro-ph 0109258]. It is found that the power of the Gemini/ AO system is comparable, with some limits, to that of the HST/NICMOS.