## Blogs about: Normality In Product

#### Cartesian Products of Two Paracompact Spaces - Continued

: Consider the real line with a topology finer than the usual topology obtained by isolating each poin … more →

#### Cartesian Products of Two Paracompact Spaces

: In some previous posts we discuss examples surrounding the Michael line showing that the product of … more →

#### The Michael Line and the Continuum Hypothesis

: There exist a Lindelof space and a separable metric space such that their Cartesian product is not n … more →

#### Bernstein Sets and the Michael Line

: Let be the Michael line and let be the set of all irrational numbers with the Euclidean topology. In … more →

#### Finite and Countable Products of the Michael Line

: Consider the real number line with a topology stronger than the Euclidean topology such that the irr … more →

#### Michael Line Basics

: Like the Sorgenfrey line, the Michael line is a classic counterexample that is covered in standard t … more →

#### Alexandroff Double Circle

: We discuss the Alexandroff double circle, which is a compact and non-metrizable space. A theorem abo … more →

#### A proof about the Michael Line

: The original post about the Michael line is now replaced by the following newer posts. You can go to … more →

#### A note about sigma-product of compact spaces

: This is a basic discussion on products of compact spaces. Let be a product space and let . The produ … more →

#### On Spaces That Can Never Be Dowker

: A Dowker space is a normal space for which the product with the closed unit interval is not normal. … more →

#### Perfectly Normal Spaces Can Never Be Dowker Spaces

: The Dowker’s theorem states that for a normal space , is normal if and only if is countably pa … more →

#### A Theorem About Hereditarily Normality

: Let be either the closed unit interval or . Let be any one of the following spaces: , , Michael Line … more →

#### Dowker's Theorem

: Let be the closed unit interval . In 1951, Dowker proved that for normal spaces , is normal if and o … more →

#### No Hereditarily Normalilty In Uncountable Product

: In a previous post, I showed that the uncountable product of the space of the integers is not normal … more →

#### Normal x Compact Needs Not be Normal

: This is to present a non-normal cross product where one factor is a normal space and the other facto … more →

#### Lindelof x Metric Needs Not Be Normal

: In a previous post, an example for Paracompact x Metric needs not be normal was given. The example i … more →

#### A Discussion About The Michael Line

: The original post was a basic discussion of the Michael line. It was written back in Oct 2009 and is … more →

#### Michael Line x Irrationals Is Not Normal — 2 comments

: The original post was about a proof that the product of the Michael line and the space of irrational … more →

#### The Example of the Uncountable Product of the Unit Interval

: Let . In a previous post, I showed that is not hereditarily separable. I would like to make an obser … more →

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