Munkres topology Section 16 Solutions
dbFin
2000 Munkres
Topology: Solutions > Chapter 2 Topological
Spaces and Continuous Functions
Categories:
Mathematics
,
Topology
by
Vadim
2011/02/23
Munkres, Section 12 Topological Spaces
No exercises.
Munkres, Section 13 Basis for a Topology
1 For every
there is an open set
such that
, therefore,
is open and
, i.e.
.
2 Let us enumerate the topologies by columns, i.e. we give numbers 1-3 for the first column from top to
bottom, 4-6 for the second column, and 7-9 for the third column. Let > be the partial relation between any
two topologies that indicates that the topology on the left side is finer [larger] than the topology on the right
side. The finer [the larger] topology is the one with the dust not the gravel. Here we list all maximal ordered
subsets of the set of topologies of Figure 12.1 ordered by >: 1