In 1998, J. Pawlicowski [6] presented a forcing free proof of a conjecture of Mycielski [4] that the fundamental group of a connected locally connected compact metric space is either finitely generated or has the power of the continuum. In this talk, we show that Mycielski’s conjecture is hold, also for higher homotopy groups. J. W. Morgan and I. Morrison [2] among presenting a Van-Kampen theorem for weak joins proved that the canonical homomorphism is injective, where H is the weak join of the Xi (as a special case H can be considered the Hawaiian earring). Here, we extend the injectivity of  to higher homotopy groups with some conditions on the Xi

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