• 대한수학회보
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• 제23권2호
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• pp.91-102
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• 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.).

• 충청수학회지
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• 제26권4호
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• pp.781-786
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• 2013

Let * be a star-operation on an integral domain R. We show that if R is a $*_{\omega}$-Noetherian domain, then quasi-$*_{\omega}$-invertible prime $*_{\omega}$-ideals of R are minimal, and prime ideals of R minimal over a $*_{\omega}$-invertible $*_{\omega}$-ideal are minimal.

• 대한수학회보
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• 제41권2호
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• pp.319-326
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• 2004

In this article, we investigate invertible interpolation problems in Alg(equation omitted) : Let(equation omitted) be a subspace lattice on a Hilbert space H and let X and Y be operators acting on H. When does there exist an invertible operator A in Alg(equation omitted) such that AX = Y?

• 대한수학회지
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• 제46권2호
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• pp.257-269
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• 2009

A ring R is a weakly stable ring provided that aR + bR = R implies that there exists $y\;{\in}\;R$ such that $a\;+\;by\;{\in}\;R$ is right or left invertible. In this article, we characterize weakly stable rings by virtue of $2{\times}2$ invertible matrices over them. It is shown that a ring R is a weakly stable ring if and only if for any $A\;{\in}GL_2(R)$, there exist two invertible lower triangular L and K and an invertible upper triangular U such that A = LUK, where two of L, U and K have diagonal entries 1. Related results are also given. These extend the work of Nagarajan et al.

• 충청수학회지
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• 제25권4호
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• pp.609-615
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• 2012

In the current paper, we establish the relationship between the powers of an invertible matrix and the powers of its inverse. More precisely, we prove that if A is an invertible matrix and, if $A^n\;=\;(A_{i,j}(n))$ for all positive integer n, then $A^{-n}\;=\;(A_{i,j}{(-n))$.

• Journal of applied mathematics & informatics
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• 제12권1_2호
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• pp.359-365
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. In this article, we investigate invertible interpolation problems in CSL-Algebra AlgL : Let L be a commutative subspace lattice on a Hilbert space H and x and y be vectors in H. When does there exist an invertible operator A in AlgL suth that An = ㅛ?

• 충청수학회지
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• 제32권4호
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• pp.529-535
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• 2019

In this article, we study the dynamics of invertible iterated function systems on compact spaces. We prove the equivalences for the notions of expansiveness on invertible iterated function systems.

• 대한수학회보
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• 제41권3호
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• pp.413-418
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• 2004

Invertible and isometric composition operators acting on vector-valued Hardy space $H^2$(E) are characterized.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.551-558
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• 2004

We shall discuss some properties of quasi-homomorphisms associated with automata. We shall give some characterizations in terms of characteristic semigroups for regular and invertible attomata.

• 대한수학회보
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• 제48권6호
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• pp.1207-1218
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• 2011

Let * be a star-operation on an integral domain R, and let $\mathfrak{I}_*^+(R)$ be the semigroup of *-invertible integral *-ideals of R. In this article, we introduce the concept of a *-coatom, and we then characterize when $\mathfrak{I}_*^+(R)$ is a free semigroup with a set of free generators consisting of *-coatoms. In particular, we show that $\mathfrak{I}_*^+(R)$ is a free semigroup if and only if R is a Krull domain and each ${\upsilon}$-invertible ${\upsilon}$-ideal is *-invertible. As a corollary, we obtain some characterizations of *-Dedekind domains.