• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.635-646
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• 2024

In this research work, we introduce and investigate four innovative types of soft spaces, pushing the boundaries of traditional spatial concepts. These new types of soft spaces are named as soft T_b space, soft T^#_b space, soft T^##_b space and soft_αT^#_b space. Through rigorous analysis and experimentation, we uncover and propose distinct characteristics that define and differentiate these spaces. In this research work, we have established that every soft $T_{\frac{1}{2}}$ space is a soft _αT^#_b space, every soft T_b space is a soft _αT^#_b space, every soft T^#_b space is a soft _αT^#_b space, every soft T_b space is a soft T^#_b space, every soft T^#_b space is a soft T^##_b space, every soft $T_{\frac{1}{2}}$ space is a soft ^#T_b space and every soft T_b space is a soft #T_b space.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.749-763
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• 2022

Let C[0, T] denote an analogue of Weiner space, the space of real-valued continuous on [0, T]. In this paper, we investigate the translation of time interval [0, T] defining the analogue of Winer space C[0, T]. As applications of the result, we derive various relationships between the analogue of Wiener space and its product spaces. Finally, we express the analogue of Wiener measures on C[0, T] as the analogue of Wiener measures on C[0, s] and C[s, T] with 0 < s < T.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.787-795
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• 2001

For the generalized nilpotent spaces, e.g. the locally nilpotent space, the residually locally nilpotent space and the space satisfying the condition ($T^{*}$) or ($T^{**}$), we find the pullback property of them. Furthermore we investigate some fiber properties of the space satisfying the condition ($T^{*}$) or ($T^{**}$), especially locally nilpotent space.

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.269-280
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• 1998

Elementary properties of the sequence space l(s, t) are studied with applications to Hardy space theory.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.3
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• pp.245-259
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• 2007

We define and study a concept of $T^f$-space for a map, which is a generalized one of a T-space, in terms of the Gottlieb set for a map. We show that X is a $T_f$-space if and only if $G({\Sigma}B;A,f,X)=[{\Sigma}B,X]$ for any space B. For a principal fibration $E_k{\rightarrow}X$ induced by $k:X{\rightarrow}X^{\prime}$ from ${\epsilon}:PX^{\prime}{\rightarrow}X^{\prime}$, we obtain a sufficient condition to having a lifting $T^{\bar{f}}$-structure on $E_k$ of a $T^f$-structure on X. Also, we define and study a concept of co-$T^g$-space for a map, which is a dual one of $T^f$-space for a map. We obtain a dual result for a principal cofibration $i_r:X{\rightarrow}C_r$ induced by $r:X^{\prime}{\rightarrow}X$ from ${\iota}:X^{\prime}{\rightarrow}cX^{\prime}$.

• Journal of the Chungcheong Mathematical Society
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• v.16 no.1
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• pp.61-71
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• 2003

We obtain a necessary condition for splitting T-space off a space in terms of cyclic maps, and also obtain a necessary condition for splitting co-T-spaces in terms of cocyclic maps.

• Journal of the Korean Society of Industry Convergence
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• v.22 no.1
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• pp.39-45
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• 2019

We propose an active color model based method for tracking motions of multiple human using a networked multiple-camera system in IoT space as a human-robot coexistent system. An IoT space is a space where many intelligent devices, such as computers and sensors(color CCD cameras for example), are distributed. Human beings can be a part of IoT space as well. One of the main goals of IoT space is to assist humans and to do different services for them. In order to be capable of doing that, IoT space must be able to do different human related tasks. One of them is to identify and track multiple objects seamlessly. In the environment where many camera modules are distributed on network, it is important to identify object in order to track it, because different cameras may be needed as object moves throughout the space and IoT space should determine the appropriate one. This paper describes appearance based unknown object tracking with the distributed vision system in IoT space. First, we discuss how object color information is obtained and how the color appearance based model is constructed from this data. Then, we discuss the global color model based on the local color information. The process of learning within global model and the experimental results are also presented.

• Honam Mathematical Journal
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• v.27 no.1
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• pp.101-113
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• 2005

We define and study a concept of $T_A$-space which is closely related to the generalized Gottlieb group. We know that X is a $T_A$-space if and only if there is a map $r:L(A,\;X){\rightarrow}L_0(A,\;X)$ called a $T_A$-structure such that $ri{\sim}1_{L_0(A,\;X)}$. The concepts of $T_{{\Sigma}B}$-spaces are preserved by retraction and product. We also introduce and study a dual concept of $T_A$-space.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.465-475
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• 1996

Fix t > 0. Denote by $C^t$ the space of $R$-valued continuous functions x on [0,t]. Let $C_0^t$ be the Wiener space - $C_0^t = {x \in C^t : x(0) = 0}$ - equipped with Wiener measure m. Let F be a function from $C^t to C$.

• Communications of the Korean Mathematical Society
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• v.18 no.4
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• pp.677-685
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• 2003

Let M be the vector space of all real S-measurable functions defined on a measure space (X, S, $\mu$). In this paper, we investigate some topological structure of T on M. Indeed, (M, T) becomes a topological vector space. Moreover, if $\mu$, is ${\sigma}-finite$, we can define a complete invariant metric on M which is compatible with the topology T on M, and hence (M, T) becomes a F-space.