标题： 关于环映射的一致轻性与收敛到同胚 显示英文标题

标题： On uniformly lightness of ring mappings and convergence to a homeomorphism

摘要： 一族映射被称为一致轻的，如果在这族映射下连续统的像不能在该族映射序列的作用下收缩到一点。 本文研究了一族满足上模不等式的同胚映射的一致轻性问题。我们证明了，如果定义这族映射的模估计中的主函数在几乎所有的球面上可积，则这族同胚映射满足上述一致轻性的条件。 在相同条件下，我们还证明了这族同胚映射是一致开的，即它们的像是一个固定半径的球，且该半径与每个映射无关。 作为所得结果的应用，我们证明了关于同胚映射一致收敛到一个同胚映射的断言。 显示英文摘要

摘要： A family of mappings is called uniformly light if the image of the continuum under these mappings cannot be contracted to a point under the sequence of mappings of the family. In this paper, we are interested in the problem of the uniform lightness of a family of homeomorphisms satisfying upper moduli inequalities. We have shown that a family of such homeomorphisms satisfies the above-mentioned condition of uniform lightness if the majorant participating in the modulus estimate defining the family is integrable over almost all spheres. Under the same conditions, we show that this family of homeomorphisms is uniformly open, i.e., their image contains a ball of fixed radius, independent of each mapping separately. As an application of the results obtained, we have proved the assertion about the uniform convergence of homeomorphisms to a homeomorphism.