Box products are often discretely generated

Tkachuk, Vladimir V.; Wilson, Richard G.

doi:10.1016/j.topol.2011.09.004

Cited by 8 publications

(2 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Notice that first countable spaces are discretely generated. Other examples of discretely generated spaces include box products of monotonically normal spaces ( [19,Theorem 26]) and countable products of monotonically normal spaces ([1, Corollary 2.6]). Also, a compact dyadic space is discretely generated if and only if it is metrizable ([19, Theorem 2.1]).…”

Section: Introductionmentioning

confidence: 99%

Remote Filters and Discretely Generated Spaces

Hernández-Gutiérrez

2013

Preprint

View full text Add to dashboard Cite

Alas, Junqueira and Wilson asked whether there is a discretely generated locally compact space whose one point compactification is not discretely generated and gave a consistent example using CH. Their construction uses a remote filter in ω× ω 2 with a base of order type ω 1 when ordered modulo compact subsets. In this paper we study the existence and preservation (under forcing extension) of similar types of filters, mainly using small uncountable cardinals. With these results we show that the CH example can be constructed in more general situations.

show abstract

Section: Introductionmentioning

confidence: 99%

Remote Filters and Discretely Generated Spaces

Hernández-Gutiérrez

2013

Preprint

View full text Add to dashboard Cite

show abstract

“…First countable spaces are clearly discretely generated and in fact spaces with relatively rich structures are discretely generated. For example, it has been shown that countable products and box products of monotonically normal spaces are discretely generated ( [21], [2]). Also, notice that the definitions of discretely generated and weakly discretely generated spaces are similar to the classic notions of Frechét-Urysohn spaces and sequential spaces, respectively, with the advantage that there is no bound for tightness (see Example 3.5 and Proposition 3.6 in [14]).…”

mentioning

confidence: 99%

Far points and discretely generated spaces

Dow

Hernández-Gutiérrez

2019

Colloq. Math.

View full text Add to dashboard Cite

We give a partial solution to a question by Alas, Junqueria and Wilson by proving that under PFA the one-point compactification of a locally compact, discretely generated and countably tight space is also discretely generated. After this, we study the cardinal number given by the smallest possible character of remote and far sets of separable metrizable spaces. Finally, we prove that in some cases a countable space has far points.0.1. Question [2] Let X be a locally compact and discretely generated space. Is the one-point compactification of X also discretely generated?So far, this question has been answered consistently in the negative. First countable counterexamples have been constructed using CH [2] or the existence of a Souslin line [1]. Later, it was shown in [17] that a similar construction could be carried out assuming the cardinal equation p = cof (M); the resulting space has an Date: October 15, 2018. 2010 Mathematics Subject Classification. 54D35, 54A25, 54G12, 54D80, 03E10, 03E75.

show abstract