Finding the maximum area of isosceles triangle

at.algebraic topology – Covering picture of a linked CW-complex necessity not breathe a CW-complex Answer

Hello expensive customer to our community We will proffer you an answer to this query at.algebraic topology – Covering picture of a linked CW-complex necessity not breathe a CW-complex ,and the respond will breathe typical by way of documented info sources, We welcome you and proffer you fresh questions and solutions, Many customer are questioning concerning the respond to this query.

at.algebraic topology – Covering picture of a linked CW-complex necessity not breathe a CW-complex

This query is already requested right here MSE, and there’s an respond primarily based on some surmise(in all probability quiet launch). I’m posting the identical query for a counterexample(if any, not primarily based on such surmise).


Problem: Let $X$ breathe a linked CW-complex, and $Y$ breathe a linked topological area. Suppose $p: Xto Y$ is a protecting map. Does there
live a CW-structure on $Y$? More typically, is $Y$ homotopically equal to a CW-complex?

Note that the opposite route is limpid: Any protecting of a linked CW-complex can at all times breathe given a CW-structure, lifting the traits map of cells of abject area such that the protecting map is a mobile map.

I consider that the respond to the above drawback is not any, however I’ve no counterexample.

$bullet$ Notice that $Y$ is regionally path-connected because the protecting map is an area homeomorphism, therefore $Y$ is path-connected too. So, we cannot deem areas ${0}cupleft{frac{1}{n}:ninBbb Nright}$ or Topologist Sine Curve as $Y$. Notice that each ${0}cupleft{frac{1}{n}:ninBbb Nright}$ or Topologist Sine round are usually not homotopically equal to a CW-complex.

$bullet$ Similarly, we cannot deem the Hawaiian Earring(this isn’t semi-locally merely linked) as $Y$: The linked CW-complex $X$ has the common mask in order that $X$ is semi-locally merely linked, however the property “semi-locally simply connected” is preserved below an area homeomorphism.

So, I’m speed out of examples. Any ameliorate will breathe appreciated. Thanks in forward.

we are going to proffer you the answer to at.algebraic topology – Covering picture of a linked CW-complex necessity not breathe a CW-complex query by way of our community which brings all of the solutions from a number of dependable sources.

Add comment