• Journal of the Chungcheong Mathematical Society
• /
• v.36 no.4
• /
• pp.289-296
• /
• 2023

When G is an abelian group, we use the notation M(G, n) to denote the Moore space. The space X is the wedge product space of Moore spaces, given by X = M(ℤ_q, n+ 2) ∨ M(ℤ_q, n+ 1) ∨ M(ℤ_q, n). We determine the self-homotopy classes group [X, X] and the self-homotopy equivalence group 𝓔(X). We investigate the subgroups of [M_j , M_k] consisting of homotopy classes of maps that induce the trivial homomorphism up to (n + 2)-homotopy groups for j ≠ k. Using these results, we calculate the subgroup 𝓔^dim_#(X) of 𝓔(X) in which all elements induce the identity homomorphism up to (n + 2)-homotopy groups of X.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.4
• /
• pp.471-481
• /
• 2008

We develop a new function space $L_{\alpha}(X)$ that generalizes the classical Lebesgue space $L^p(X)$. The generalization is focused on a better explanation of the flux terms arising from many dynamics.

• Journal of the Chungcheong Mathematical Society
• /
• v.35 no.3
• /
• pp.255-267
• /
• 2022

Uniform space is a generalization of metric space. The main purpose of this paper is to extend several results contained in [5, 6] which have for an expansive homeomorphism with the pseudo orbit tracing property(POTP in short) on a compact metric space (X, d) for an expansive homeomorphism with the POTP on a compact uniform space (X, 𝒰). we characterize stable and unstable sets, sink and source and saddle, recurrent points for an expansive homeomorphism which has the POTP on a compact uniform space (X, 𝒰).

• Kyungpook Mathematical Journal
• /
• v.47 no.1
• /
• pp.69-76
• /
• 2007

Let $f$ denote a mapping from an orthogonality space ($\mathcal{X}$, ${\bot}$) into a real Banach space $\mathcal{Y}$. In this paper, we prove the Hyers-Ulam-Rassias stability of the orthogonally cubic functional equations $f(2x+y)+f(2x-y)=2f(x+y)+2f(x-y)+12f(x)$ and $f(x+y+2z)+f(x+y-2z)+f(2x)+f(2y)=2f(x+y)+4f(x+z)+4f(x-z)+4f(y+z)+4f(y-z)$, where $x{\bot}y$, $y{\bot}z$, $x{\bot}z$.

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

• Journal of the Korean Statistical Society
• /
• v.10
• /
• pp.83-90
• /
• 1981

Let (X, A) be a measurable space, i.e. X is a non-empty set and A is a $\sigma$-field of subsets of X. Let $\Omega$ be a parameter space and P be a family of probability measures $P_\theta, \theta \in \Omega$ defined on (X, A).

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.1
• /
• pp.161-173
• /
• 2013

This paper is concerned with the space $\mathcal{K}_{w^*}(X^*,Y)$ of $weak^*$ to weak continuous compact operators from the dual space $X^*$ of a Banach space X to a Banach space Y. We show that if $X^*$ or $Y^*$ has the Radon-Nikod$\acute{y}$m property, $\mathcal{C}$ is a convex subset of $\mathcal{K}_{w^*}(X^*,Y)$ with $0{\in}\mathcal{C}$ and T is a bounded linear operator from $X^*$ into Y, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\{S{\in}\mathcal{C}:{\parallel}S{\parallel}{\leq}{\parallel}T{\parallel}\}}^{{\tau}_{\mathcal{c}}}$, where ${\tau}_{\mathcal{c}}$ is the topology of uniform convergence on each compact subset of X, moreover, if $T{\in}\mathcal{K}_{w^*}(X^*, Y)$, here $\mathcal{C}$ need not to contain 0, then $T{\in}\bar{\mathcal{C}}^{{\tau}_{\mathcal{c}}}$ if and only if $T{\in}\bar{\mathcal{C}}$ in the topology of the operator norm. Some properties of $\mathcal{K}_{w^*}(X^*,Y)$ are presented.

• Bulletin of the Korean Mathematical Society
• /
• v.23 no.2
• /
• pp.91-102
• /
• 1986

A topological space (X,.tau.) is called invertible [7] if for each proper open set U in (X,.tau.) there exists a homoemorphsim h:(X,.tau.).rarw.(X,.tau.) such that h(X-U).contnd.U. Doyle and Hocking [7] and Levine [13], as well as others have investigated properties of invertible spaces. Recently, Crosseley and Hildebrand [5] have introduced the concept of semi-invertibility, which is weaker than that of invertibility, by replacing "homemorphism" in the definition of invertibility with "semihomemorphism", A space (X,.tau.) is said to be semi-invertible if for each proper semi-open set U in (X,.tau.) there exists a semihomemorphism h:(X,.tau.).rarw.(X,.tau.) such that h(X-U).contnd.U. The purpose of the present article is to introduce the class of almost-invertible spaces containing the class of semi-invertible spaces and to investigate its properties. One of the primary concerns will be to determine when a given local property in an almost-invertible space is also a global property. We point out that many of the results obtained can be applied in the cases of semi-invertible spaces and invertible spaces. For example, it is shown that if an invertible space (X,.tau.) has a nonempty open subset U which is, as a subspace, H-closed (resp. lightly compact, pseudocompact, S-closed, Urysohn, Urysohn-closed, extremally disconnected), then so is (X,.tau.).hen so is (X,.tau.).

• Journal of the Korean Mathematical Society
• /
• v.33 no.4
• /
• pp.763-775
• /
• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• Bulletin of the Korean Space Science Society
• /
• 1994.09a
• /
• pp.23-23
• /
• 1994

No Abstract. See Full-text