拓扑空间中的连续逼近选择和几乎不动点

本文研究连续逼近选择问题 研究结果表明 ,几乎下半连续的集值映射有连续逼近选择 .从而 ,著名的Michael连续逼近选择定理被改进 .应用这个结果 ,一个几乎不动点定理被获得     

Erratum to “Normality and countable paracompactness of hyperspaces of ordinals” [Topology Appl. 154 (2007) 358-362]

We correct the proof of Theorem 8 in “Normality and countable paracompactness of hyperspaces of ordinals” [Topology Appl. 154 (2007) 358-362].     

A new look at some classical theorems on continuous functions on normal spaces

A sufficient condition for the strict insertion of a continuous function between two comparable upper and lower semicontinuous functions on a normal space is given. Among immediate corollaries are the classical insertion theorems of Michael and Dowker. Our insertion lemma also provides purely topological proofs of some standard results on closed subsets of normal spaces which normally depend upon uniform convergence of series of continuous functions. We also establish a Tietze-type extension theorem characterizing closed G _δ -sets in a normal space. This research was supported by the Ministry of Education and Science of Spain and FEDER under grant MTM2006-14925-C02-02. The first named author also acknowledges financial support from the University of the Basque Country under grant UPV05/101.     

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。     

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.     

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.

     

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.     

The continuity of the inversion and the structure of maximal subgroups in countably compact topological semigroups

We search for conditions on a countably compact (pseudocompact) topological semigroup under which: (i) each maximal subgroup H(e) in S is a (closed) topological subgroup in S; (ii) the Clifford part H(S) (i.e. the union of all maximal subgroups) of the semigroup S is a closed subset in S; (iii) the inversion inv: H(S) → H(S) is continuous; and (iv) the projection π: H(S) → E(S), π: x ↦ xx ⁻¹, onto the subset of idempotents E(S) of S, is continuous.      

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.