JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (10): 72-76.doi: 10.6040/j.issn.1671-9352.0.2016.571

Previous Articles     Next Articles

D-properties of Finite unions of spaces with point countable weak bases and satisfying open(G)

GUO Hong-feng1,2, LI Yu-si1, SUN Wei-hua3   

  1. 1. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014, Shandong, China;
    2. School of Control Science and Engineering, Shandong University, Jinan 250061, Shandong, China;
    3. School of Mathematics and Statistics, Shandong University(Weihai), Weihai 264209, Shandong, China
  • Received:2016-12-05 Online:2017-10-20 Published:2017-10-12

PDF (PC)

407

Abstract: The relation between point-countable weak bases and D-property is studied. It is shown that, if a space X of countable tightness is the union of finitely many subspaces Xi with point-countable weak base Ti={Ti(x):x∈Xi} satisfying Ti(x)∩Ti(y)=Ø for any distinct x,y∈X, then X is a D-space. And then the relation is studied between open(G)and D-property. We obtain that, if X=X1∪X2, where both X1 and X2 satisfy open(G), then X1^-∩X2^- satisfies open(G). With the help of this result, a detailed proof is shown at last for the result that the union of finitely many subspaces satisfying open(G)is a D-space.

Key words: weak base, countable tightness, open(G), D-space

CLC Number: 

  • O189.1
[1] VAN DOUWEN E K, PFEFFER W. Some properties of the Sorgenfrey line and related spaces[J]. Pacific Journal of Mathematics, 1979, 81(2):371-377.
[2] ARHANGELSKII A V. D-spaces and finite unions[J]. Proceedings of the American Mathematical Society, 2004, 132(7):2163-2170.
[3] SOUKUP D, SZEPTYCKI P J. The union of two D-spaces need not be D[J]. Fundamenta Mathematicae, 2013, 220:129-137.
[4] ARHANGELSKII A V, BUZYAKOVA R Z. Addition theorems and D-spaces[J]. Commentationes Mathematicae Universitatis Carolinae, 2002, 43(4):653-663.
[5] ZHANG Xin, GUO Hongfeng. The D-property of finite unions of t-metrizable spaces and certain function spaces[J]. Journal of Function Spaces, 2013. Doi: 10.1155/2013/612954.
[6] PENG Liang-Xue. The D-property of some Lindelöf spaces and related conclusions[J]. Topology and its Applications, 2007, 154:469-475.
[7] BURKE D. Weak bases and D-spaces[J]. Commentationes Mathematicae Universitatis Carolinae, 2007, 48:281-289.
[8] ARHANGELSKII A V. Mappings and spaces[J]. Russian Mathematical Surveys, 1966, 21(4):115-162.
[9] COLLINS P J, REED G M, Roscoe A W. The point-countable base problem[M] // VAN MILL J, REED G M. Open problems in topology. Amsterdam: Elsevier, 1990: 237-250.
[10] GRUENHAGE G. A note on D-spaces[J]. Topology and its Applications, 2006, 153(13):2229-2240.
[11] ENGELKING R. General topology[M]. Warsaw: Polish Scientific Publishers, 1977.
[12] 郭洪峰,张新. 对两种重要空间类D-空间性质的研究[J]. 山东大学学报(理学版), 2008, 43(1):88-90. GUO Hongfeng, ZHANG Xin. Research on two important classes of D-spaces[J]. Journal of Shandong University(Natural Science), 2008, 43(1):88-90.
[1] LIU Shi-Qin1, CHEN Hai-Yan2. On  g-metrizable spaces and weak open mappings   [J]. J4, 2010, 45(3): 102-104.
[2] GUO Hong-feng,ZHANG Xin . Research on two important classes of D-spaces [J]. J4, 2008, 43(1): 88-90 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd