Realizing spaces as path-component spaces

Preprint English OPEN
Banakh, Taras; Brazas, Jeremy;
  • Subject: Mathematics - General Topology | Mathematics - Algebraic Topology | 55Q52, 58B05, 54B15, 22A05, 54C10, 54G15

The path component space of a topological space $X$ is the quotient space $\pi_0(X)$ whose points are the path components of $X$. We show that every Tychonoff space $X$ is the path-component space of a Tychonoff space $Y$ of weight $w(Y)=w(X)$ such that the natural quot... View more
  • References (27)
    27 references, page 1 of 3

    [1] A. Arhangel'skii, M. Tkachenko, Topological Groups and Related Structures, Series in Pure and Applied Mathematics, Atlantis Studies in Mathematics, 2008.

    [2] T. Banakh, M. Vovk, M.R. Wo┬┤ jcik, Connected economically metrizable spaces, Fund. Math. 212 (2011), 145-173.

    [3] J. Brazas, Homotopy Mapping Spaces, Ph.D. Dissertation, University of New Hampshire, 2011.

    [4] J. Brazas, The topological fundamental group and free topological groups, Topology Appl. 158 (2011) 779-802.

    [5] J. Brazas, The fundamental group as a topological group, Topology Appl. 160 (2013) 170-188.

    [6] J. Brazas, Open subgroups of free topological groups, Fundamenta Mathematicae 226 (2014) 17-40.

    [7] J. Brazas, P. Fabel, On fundamental groups with the quotient topology, J. Homotopy and Related Structures 10 (2015) 71-91.

    [8] J. Calcut, J. McCarthy, Discreteness and homogeneity of the topological fundamental group, Topology Proc. 34 (2009) 339-349.

    [9] R.J. Daverman, Decompositions of manifolds, Pure and Applied Mathematics, vol. 124, Academic Press Inc., Orlando, FL, 1986.

    [10] K. Eda, K. Kawamura, The fundamental groups of one-dimensional spaces, Topology Appl. 87 (1998) 163-172.

  • Metrics
    No metrics available
Share - Bookmark