User Jeremy Brazas

50 votes

Fundamental group as topological group

answered Jun 1, 2010 at 13:22

38 votes

Is the Hurewicz theorem ever used to compute abelianizations?

answered Jan 26, 2017 at 15:52

37 votes

Is there a "universal" connected compact metric space?

answered Nov 12, 2017 at 4:29

37 votes

Accepted

Are the higher homotopy groups of the Hawaiian earring trivial?

answered Apr 20, 2014 at 2:29

21 votes

Accepted

Universal covering space for non-semilocally simply connected spaces

answered Nov 3, 2012 at 16:15

18 votes

Accepted

Is a space with no covering spaces simply connected?

answered Mar 13, 2011 at 16:54

16 votes

Accepted

Does $\pi_1$ have a right adjoint?

answered Nov 8, 2010 at 22:30

15 votes

Accepted

when is a locally homeo a covering map?

answered Oct 11, 2012 at 21:52

14 votes

Serre fibration vs Hurewicz fibration

answered Jun 6, 2016 at 21:27

12 votes

Accepted

In a subset of $\mathbb{R}^2$ which is not simply connected does there exist a simple loop that does not contract to a point?

answered Aug 10, 2019 at 22:12

10 votes

Accepted

Fundamental groups and homology groups of closed subsets of the plane

answered Oct 27, 2012 at 13:38

9 votes

Fundamental group of R^2 minus the (ir)rationals

answered Nov 20, 2010 at 21:38

9 votes

Accepted

Free product decompositions of the fundamental group of Hawaiian Earrings

answered Feb 21, 2020 at 20:04

8 votes

Induced homomorphisms on fundamental groups

answered Oct 10, 2013 at 1:32

8 votes

Accepted

Construction of the universal covering space via compact-open topology

answered Mar 3, 2021 at 17:26

8 votes

Accepted

A topological tree is weakly contractible

answered Dec 19, 2022 at 14:21

7 votes

Which spaces have enough curves

answered Jun 16, 2016 at 10:20

7 votes

Accepted

Lifts across covering maps

answered May 11, 2014 at 22:58

6 votes

Accepted

What is an example of a non-regular, totally path-disconnected Hausdorff space?

answered May 4, 2010 at 17:38

6 votes

Accepted

Homotopy equivalent fibers and Fibrations

answered May 3, 2020 at 23:36

5 votes

The union of all coreflective Cartesian closed subcategories of $\mathbf{Top}$

answered Apr 1, 2019 at 18:37

5 votes

Accepted

A generalization of covering spaces to fiber bundles with totally path-disconnected fibers

answered May 10, 2014 at 19:45

5 votes

Applications of space filling curves

answered May 7, 2016 at 23:50

5 votes

Accepted

Path-lifting property: function space interpretation

answered May 29, 2018 at 19:59

5 votes

Examples of transfinite towers

answered Mar 17, 2019 at 17:53

4 votes

A question on Hawaiian earring group

answered Jan 27, 2020 at 0:53

4 votes

Accepted

Are open sets determined by paths?

answered Feb 4, 2020 at 13:06

4 votes

Accepted

fundamental groups of complements to countable subsets of the plane

answered Feb 20, 2020 at 14:30

4 votes

Accepted

Example similar to the Griffiths twin cone but with fundamental group that allows surjection onto $\mathbb Z$

answered Jan 19, 2019 at 21:52

4 votes

Is the wedge sum of two cones over the hawaiian earring contractible?

answered Dec 22, 2012 at 0:56

Stack Exchange Network

47 Answers

Fundamental group as topological group

Is the Hurewicz theorem ever used to compute abelianizations?

Is there a "universal" connected compact metric space?

Are the higher homotopy groups of the Hawaiian earring trivial?

Universal covering space for non-semilocally simply connected spaces

Is a space with no covering spaces simply connected?

Does $\pi_1$ have a right adjoint?

when is a locally homeo a covering map?

Serre fibration vs Hurewicz fibration

In a subset of $\mathbb{R}^2$ which is not simply connected does there exist a simple loop that does not contract to a point?

Fundamental groups and homology groups of closed subsets of the plane

Fundamental group of R^2 minus the (ir)rationals

Free product decompositions of the fundamental group of Hawaiian Earrings

Induced homomorphisms on fundamental groups

Construction of the universal covering space via compact-open topology

A topological tree is weakly contractible

Which spaces have enough curves

Lifts across covering maps

What is an example of a non-regular, totally path-disconnected Hausdorff space?

Homotopy equivalent fibers and Fibrations

The union of all coreflective Cartesian closed subcategories of $\mathbf{Top}$

A generalization of covering spaces to fiber bundles with totally path-disconnected fibers

Applications of space filling curves

Path-lifting property: function space interpretation

Examples of transfinite towers

A question on Hawaiian earring group

Are open sets determined by paths?

fundamental groups of complements to countable subsets of the plane

Example similar to the Griffiths twin cone but with fundamental group that allows surjection onto $\mathbb Z$

Is the wedge sum of two cones over the hawaiian earring contractible?