Blogs about: Normality In Product

Featured Blog

Cartesian Products of Two Paracompact Spaces – Continued

Consider the real line with a topology finer than the usual topology obtained by isolating each point in where is the set of all irrational numbers. The real line with this finer topology is called th… more →

Dan Ma's Topology Blog

Cartesian Products of Two Paracompact Spaces - Continued

Dan Ma wrote 6 months ago: Consider the real line with a topology finer than the usual topology obtained by isolating each poin … more →

Tags: Basic Topology, product space, Michael Line, Paracompact space, Lindelof space, Normal space, compact space, Advanced Topics, Metrizable spaces

Cartesian Products of Two Paracompact Spaces

Dan Ma wrote 6 months ago: In some previous posts we discuss examples surrounding the Michael line showing that the product of … more →

Tags: Basic Topology, product space, Michael Line, Paracompact space, Lindelof space, Normal space, compact space, Well known examples, Advanced Topics

The Michael Line and the Continuum Hypothesis

Dan Ma wrote 6 months ago: There exist a Lindelof space and a separable metric space such that their Cartesian product is not n … more →

Tags: Basic Topology, First uncountable ordinal, Omega 1, product space, Michael Line, Lindelof space, Normal space, Well known examples, Advanced Topics

Bernstein Sets and the Michael Line

Dan Ma wrote 6 months ago: Let be the Michael line and let be the set of all irrational numbers with the Euclidean topology. In … more →

Tags: Basic Topology, product space, Michael Line, Paracompact space, Lindelof space, Normal space, Well known examples, The real line, Non-normal product

Finite and Countable Products of the Michael Line

Dan Ma wrote 6 months ago: Consider the real number line with a topology stronger than the Euclidean topology such that the irr … more →

Tags: Basic Topology, product space, Michael Line, Paracompact space, Normal space, Well known examples, Non-normal product, Topology, General Topology

Michael Line Basics

Dan Ma wrote 6 months ago: Like the Sorgenfrey line, the Michael line is a classic counterexample that is covered in standard t … more →

Tags: The real line, Basic Topology, product space, Michael Line, Paracompact space, Normal space, Well known examples, Separable metrizable, moore space

Alexandroff Double Circle

Dan Ma wrote 7 months ago: We discuss the Alexandroff double circle, which is a compact and non-metrizable space. A theorem abo … more →

Tags: Basic Topology, product space, Lindelof space, Normal space, compact space, Well known examples, Perfectly normal space, Separable space, Hereditarily normal space

A proof about the Michael Line

Dan Ma wrote 2 years ago: The original post about the Michael line is now replaced by the following newer posts. You can go to … more →

Tags: Basic Topology, product space, Michael Line, Lindelof space, Normal space, Well known examples, Non-normal product, Topology, General Topology

A note about sigma-product of compact spaces

Dan Ma wrote 3 years ago: This is a basic discussion on products of compact spaces. Let be a product space and let . The produ … more →

Tags: Basic Topology, First uncountable ordinal, product space, Paracompact space, Normal space, compact space, Omega 1, Non-normal product, Countable chain condition

On Spaces That Can Never Be Dowker

Dan Ma wrote 3 years ago: A Dowker space is a normal space for which the product with the closed unit interval is not normal. … more →

Tags: product space, Paracompact space, Normal space, compact space, Advanced Topology, Metrizable spaces, moore space, Non-normal product, Perfectly normal space

Perfectly Normal Spaces Can Never Be Dowker Spaces

Dan Ma wrote 3 years ago: The Dowker’s theorem states that for a normal space , is normal if and only if is countably pa … more →

Tags: product space, Normal space, Advanced Topology, Non-normal product, Countably paracompact space, Dowker space, Topology, General Topology, Point-Set Topology

A Theorem About Hereditarily Normality

Dan Ma wrote 3 years ago: Let be either the closed unit interval or . Let be any one of the following spaces: , , Michael Line … more →

Tags: Normal space, Advanced Topology, The Sorgenfrey Line, product space, Michael Line, Perfectly normal space, Countably paracompact space, Hereditarily normal space, Topology

Dowker's Theorem

Dan Ma wrote 3 years ago: Let be the closed unit interval . In 1951, Dowker proved that for normal spaces , is normal if and o … more →

Tags: product space, Normal space, compact space, Advanced Topology, Countably paracompact space, Dowker space, Topology, General Topology, Point-Set Topology

No Hereditarily Normalilty In Uncountable Product

Dan Ma wrote 3 years ago: In a previous post, I showed that the uncountable product of the space of the integers is not normal … more →

Tags: Basic Topology, product space, Normal space, Non-normal product, Hereditarily normal space, Topology, General Topology, Point-Set Topology

Normal x Compact Needs Not be Normal

Dan Ma wrote 3 years ago: This is to present a non-normal cross product where one factor is a normal space and the other facto … more →

Tags: Basic Topology, First uncountable ordinal, Omega 1, product space, Normal space, compact space, Well known examples, Double arrow space, Non-normal product

Lindelof x Metric Needs Not Be Normal

Dan Ma wrote 3 years ago: In a previous post, an example for Paracompact x Metric needs not be normal was given. The example i … more →

Tags: Basic Topology, product space, Michael Line, Normal space, Well known examples, Non-normal product, Topology, General Topology, Point-Set Topology

A Discussion About The Michael Line

Dan Ma wrote 3 years ago: The original post was a basic discussion of the Michael line. It was written back in Oct 2009 and is … more →

Tags: Basic Topology, product space, Michael Line, Normal space, Well known examples, Non-normal product, Perfectly normal space, Metrizable spaces, Topology

Michael Line x Irrationals Is Not Normal — 2 comments

Dan Ma wrote 3 years ago: The original post was about a proof that the product of the Michael line and the space of irrational … more →

Tags: Basic Topology, product space, Michael Line, Normal space, Well known examples, Baire category theorem, Non-normal product, Perfectly normal space, Paracompact space

The Example of the Uncountable Product of the Unit Interval

Dan Ma wrote 3 years ago: Let . In a previous post, I showed that is not hereditarily separable. I would like to make an obser … more →

Tags: Basic Topology, Product of unit interval, Normal space, product space, Non-normal product, Hereditarily normal space, Hereditarily lindelof, Topology, General Topology


Related Tags
All →

Follow this tag via RSS