关于完全仿紧空间的一些刻画

本文在Ｔ１正则的条件下得到了完全仿紧空间的一些等价刻画,并利用所得到的刻画证明了这类空间的一个可数乘积定理。     

Continuous selections as parametrically defined integrals

An analog of the classical Michael theorem on continuous single-valued selections of lower semicontinuous maps whose values are closed and convex in a Fréchet space is proved for maps into metrizable (non-locally-convex) vector spaces. It turns out that, instead of the local convexity of the whole space containing these values, it is sufficient to require that the family of values of the map be uniformly locally convex. In contrast to the standard selection theorems, the proof bypasses the process of successively improving the approximations, and the desired selection is constructed as the result of pointwise integration with respect to a suitable probability distribution.     

关于纤维一般拓扑的一点注记(英文)

Some characterizations of paracompact maps are given in this note, and some equivalent statements of collectionwise normal maps are discussed. And also we show that if f ： X→Y is a closed collectionwise normal map, and f^-1（y） is a semistratifiable subspace of X for any y ∈ Y, then f is a paracompact map.     

Completely regular paracompact reflection of locales

We give an explicit construction of the completely regular paracompact reflection pL of a completely regular locale L described as a sublocale of the Stone-tech compactification βL of L.     

Monotone normality and paracompactness

In this paper it is proved that a topological space is necessarily paracompact if it is monotonically normal and any one of the following: screenable, paralindelöf, has a G_δ-diagonal or a quasi-G_δ-diagonal or has a σ-locally-countable base.     

相对拓扑的一些性质

讨论了相对超正则的充要条件及相对拓扑空间在映射下的一些性质，并定义了两类新的相对拓扑空间，给出了它们的一些性质．     

Strong paracompactness and w- -refinability of inverse limits

In this paper we construct inverse systems of which each space is strongly paracompact and each bonding map and each projection are open and onto maps, and the limit space is paracompact and not strongly paracompact and we investigate -refinability-like properties of limit spaces of inverse systems.

     

Failure of normality in the box product of uncountably many real lines

We prove in ZFC that the box product of many copies of is neither normal nor collectionwise Hausdorff. As an addendum to the proof, we show that if the cardinality of the continuum is , then these properties also fail in the closed subspace consisting of all functions which assume the value on all but countably many indices.

     

Generalized Quasi—Variational Inequalities on Paracompact Sets

Ｔｈｉｓｐａｐｅｒｉｓｃｏｎｔｉｎｕａｔｉｏｎｓｏｆ［１］，ｗｅｓｔｉｌｌｔｏｕｓｅｍａｒｋｓａｎｄｔｅｒｍｓｉｎ［１］ａｎｄｔｈｅｏｔｈｅｒｔｅｒｍｓａｇｒｅｅｗｉｔｈ［２］ａｎｄ［３］．ＬｅｔＥａｎｄＦｂｅｔｗｏＨａｕｓｄｏｒｆｆｔｏｐｏｌｏｇｉｃａｌｖｅｃｔｏｒｓｐａｃｅｓ，ＸＥ，ＹＦｂｅｔｗｏｎｏｎｅｍｐｔｙｓｅｔｓ，ＦｂｅｔｈｅｄｕａｌｓｐａｃｅｏｆＦ，Ａ：Ｘ→２ＹａｎｄＢ：Ｙ→２Ｆｂｅｔｗｏｓｅｔ－ｖａｌｕｅｄｍａｐｐｉｎｇ，Ｔ：Ｙ→Ｘｂｅｉｎｖｅｒｔｉｂｌｅ．Ｉｎｔｈｉｓｐ…     

A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement

We get the following result. A topological space is strongly paracompact if and only if for any monotone increasing open cover of it there exists a star-finite open refinement. We positively answer a question of the strongly paracompact property.