A note on products of (weakly) discretely generated spaces

作者：Peng Liang Xue^*; Yang Chong

来源：Topology and Its Applications, 2014, 161: 354-363.

DOI：10.1016/j.topol.2013.10.038

• Discretely generated space
• Weakly discretely generated space l-Nested space
• Generalized ordered space

In the first part of this note, we mainly get the following conclusions. If X is a regular space with a nested local base at a point a of X and Y is discretely generated at a point b of Y, then X x Y is discretely generated at < a, b >. We finally show that if X is a GO-space and Y is a discretely generated space then X x Y is discretely generated.
In the last part of this note, we mainly get the following conclusions. If X is a locally compact GO-space and there exists a closed discrete set F such that for any point x is an element of X \ F, there is a neighborhood V-x of x in X such that V-x x Y is weakly discretely generated, where Y is a weakly discretely generated space, then X x Y is weakly discretely generated. If X is a locally compact GO-space such that X x Y is weakly,discretely generated and lX \ X is scattered, where lX is a linearly ordered compactification of X and Y is a weakly discretely generated space, then lX x Y is weakly discretely generated.

• 出版日期2014-1-1
• 单位北京工业大学