Abstract
A recent result in Continuum theory states that each continuum containing an Ri-set with i∈{1,2,3} is non-pseudo-contractible. In this paper, we introduce the concept of R4-continuum and mainly show a new class of non-pseudo-contractible continua, we give the relationship between R4-continua and Ri-sets with i∈{1,2,3}, as well as the relationship between R4-continua and s-points, we prove that the standard hyperspaces of a continuum containing an R4-continuum also contain an R4-continuum, and we prove that if f:X→Y is an open map between continua and Y contains an R4-continuum, then X contains an R4-continuum.
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