• 대한수학회논문집
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• 제19권3호
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• pp.519-529
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• 2004

M. Brown [2] posed an open question on the class of free homeomorphisms as follows: if f is a free homeomorphism of two manifold and k is a positive integer then is $f^{k}$ free\ulcorner In this paper we show that the answer of the open question is true.

• 대한수학회보
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• 제58권1호
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• pp.133-146
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• 2021

For pseudo-free and recurrent self-similar groups, we show that continuous orbit equivalence of inverse semigroup partial actions implies continuous orbit equivalence of group actions. Conversely, if group actions are continuous orbit equivalent, and the induced homeomorphism commutes with the shift maps on their groupoids, we obtain continuous orbit equivalence of inverse semigroup partial actions.

• 대한수학회지
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• 제44권6호
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• pp.1479-1503
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• 2007

In this paper, we study a strong k-deformation retract derived from a relative k-homotopy and investigate its properties in relation to both a k-homotopic thinning and the k-fundamental group. Moreover, we show that the k-fundamental group of a wedge product of closed k-curves not k-contractible is a free group by the use of some properties of both a strong k-deformation retract and a digital covering. Finally, we write an algorithm for calculating the k-fundamental group of a dosed k-curve by the use of a k-homotopic thinning.