不可度量化Ω-有界曲面中的同伦
Homotopy in non metrizable omega-bounded surfaces
摘要：
研究了在$ω$ -有界不可度量化流形$X,Y$之间连续函数的同伦类$[X,Y]$的刻画问题.我们定义了一个家庭的表面$X$建立的第一个八分圆$C$在$L^2$（$L$是长线和$R$的longray），并表明，$[X,R]$是双射与所谓的“适应”子集的偏序集。我们还表明，$[M,R]$可以计算一些表面$M$，不像$C$，不包含$R$。这表明，当$X,Y$是$ω$有界的不可度量化曲面时，X$中的$Y$ -方向概念与$[X,Y]$之间可能存在联系.使用了许多图片，证明非常详细。
英文摘要：
We investigate the problem of describing the homotopy classes $[X,Y]$ of continuous functions between $ω$-bounded non metrizable manifolds $X,Y$. We define a family of surfaces $X$ built with the first octant $C$ in $L^2$ ($L$ is the longline and $R$ the longray), and show that $[X,R]$ is in bijection with so called `adapted' subsets of a partially ordered set. We also show that $[M,R]$ can be computed for some surfaces $M$ that, unlike $C$, do not contain $R$. This indicates that when $X,Y$ are $ω$-bounded non metrizable surfaces, there might be a link between $[X,Y]$ and the concept of $Y$-directions in X$. Many pictures are used and the proofs are quite detailed.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
