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<p>In this paper, we establish sufficient conditions under which a densifiable metric space has the approximate fixed point property (AFPP). More precisely, we show that such a space can, in a specific sense, be approximated by a sequence of Peano continua contained within it. Under suitable conditions on these Peano continua, we prove that the AFPP holds for the given densifiable metric space. As a consequence of this result, we get the well-known Brouwer’s fixed point theorem. The AFPP is also studied for the countable product of densifiable metric spaces.</p>

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The approximate fixed point property for densifiable metric spaces

  • 期刊论文

  • 发表日期：

    2026年1月16日

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  • G. García

摘要

In this paper, we establish sufficient conditions under which a densifiable metric space has the approximate fixed point property (AFPP). More precisely, we show that such a space can, in a specific sense, be approximated by a sequence of Peano continua contained within it. Under suitable conditions on these Peano continua, we prove that the AFPP holds for the given densifiable metric space. As a consequence of this result, we get the well-known Brouwer’s fixed point theorem. The AFPP is also studied for the countable product of densifiable metric spaces.