Let X be subset of real line R and |X|=c. Consider X with topology Sorgenfrei. Space X^2 is not normal ?

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Alexander Osipov

we note that it is sufficient that there be a closed continuum discrete .

something interesting In next paper

Cenap Özel

I know that the product of Sorgenfrey line is not normal

Giuseppe Di Maio

X2 is not normal. In fact the diagonal D . y = - x is closed and discrete; Q2 is dense and countable. Apply F.B. Jones Lemma Dugundji. Page 144. or observe that C(X2) is less than or equal to c and greater than or equal to 2c .A contradiction. Ciao.Peppe

Peppe, the diagonal D . y = - x may be countable set ....

Nodirbek Kamoldinovich Mamadaliev

If X is continuum, the diagonal how can be countable?!

It can be empty....)))

yeah, for D y=-x you r right.

It must always be find closed discrete continuum subset in X^2.

the following is interesting