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Questions related from Eliza Wajch
Let me use the notation from "Axiom of Choice" by Horst Herrlich and refer to Theorem 4.55 from this book. I recall that CC(cR) is the statement that every nonempty countable family of complete...
03 March 2017 224 1 View
There are models of ZF in which some Cantor cubes are non-compact. If a Cantor cube $X= 2^J$ is non-compact, there does not exist a compactification $\alpha X$ of $X$ such that, for each $j\in...
31 October 2016 3,983 3 View
I know that It holds true in ZFC (even in ZF+DC) that every topological group is completely regular. It is also known to me that, in some models for ZF, a topology induced by a uniformity can be...
02 June 2016 1,496 2 View
It is known to me that, in some models for ZF, for an uncountable set $J$, the Cantor cube {0,1}^J can be metrizable. Unfortunately, I still do not know whether there is a model for ZF in which,...
06 December 2015 5,133 10 View
I have just discovered that a Haudorff compactification of a discrete space can fail to be completely regular in a model for ZF. A helpful paper for it is "Continuing horrors of topology without...
28 September 2015 8,860 7 View
Let us have a look at the following statement: every pathwise connected Hausdorff space is arcwise connected. It holds true in ZFC or even in ZF+an appropriate weaker form of AC. I wonder if...
23 September 2015 8,554 10 View
I know that there is a model M for ZF such that. for an uncountable set S in this model and for every collection $\{ (X_s, d_s): s\in S\}$ of metric spaces in this model, their product...
11 August 2015 3,673 8 View
Condition (7) of Theorem 4.54 in the book ``Axiom of Choice" by Horst Herrlich is the sentence: Each second countable topological space is separable. Theorem 4.54 of this book says that (7) is...
10 August 2015 5,493 4 View
In the standard proof of Hilbert projection theorem the axiom of countable choice (denoted by CC) is used. I wonder whether there is a model of ZF+ the negation of CC in which Hilbert projection...
01 January 1970 6,725 3 View
