Spaces whose 𝑛th power is weakly infinite-dimensional but whose (𝑛+1)th power is not

Pol, Elżbieta

doi:10.1090/s0002-9939-1993-1148027-5

Cited by 5 publications

(2 citation statements)

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“…Note the following results of E. Pol [84]. There exist a C-space X and a zero-dimensional space Y which is a subset of irrational numbers Irr (on the assumption of CH we can assume that Y = Irr) whose product is A-s.i.d.…”

Section: N + M and Every Possibility Can Be Achieved The Cornpacmentioning

confidence: 99%

The dimension problem for the product of infinite-dimensional spaces

Chatyrko¹

1996

J Math Sci

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Section: N + M and Every Possibility Can Be Achieved The Cornpacmentioning

confidence: 99%

The dimension problem for the product of infinite-dimensional spaces

Chatyrko¹

1996

J Math Sci

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“…For instance, see [1], [10], [11], [13], [14], [15], [? ], [22], and [23]. However, there is much less known about selective strong screenablity.…”

Section: Introductionmentioning

confidence: 99%

Selective Strong Screenability

Coombs¹

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Screenability and strong screenability were both introduced some sixty years ago by R.H. Bing in his paper Metrization of Topological Spaces. Since then, much work has been done in exploring selective screenability (the selective version of screenability). However, the corresponding selective version of strong screenability has been virtually ignored. In this paper we seek to remedy this oversight. It is found that a great deal of the proofs about selective screenability readily carry over to proofs for the analogous version for selective strong screenability. We give some examples of selective strongly screenable spaces with the primary example being Pol's space. We go on to explore a natural weakening of selective strong screenability in topological groups.We conclude with an exploration of the difficulty in extending discrete families of sets as well as giving several directions one might go in when continuing the exploration of selective strong screenability.iv

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Weakly infinite-dimensional spaces

Fedorchuk¹

2007

Russ. Math. Surv.

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Spaces whose 𝑛th power is weakly infinite-dimensional but whose (𝑛+1)th power is not

Abstract: For every natural number n we construct a metrizable separable space Y such that Y" is weakly infinite-dimensional (moreover, is a C-space) but Yn+l is strongly infinite-dimensional.

Cited by 5 publications

References 16 publications

The dimension problem for the product of infinite-dimensional spaces

The dimension problem for the product of infinite-dimensional spaces

Selective Strong Screenability

Weakly infinite-dimensional spaces

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