Perfectly Normal Non-metrizable Non
... L by recursion, so that the branch space of T is dense in L. L may have isolated points, but these are also open intervals, except for initial or final isolated points, which can conventionally be written as (∞, a) or (b, ∞), so we will also consider them to be open intervals. We form the 0’th level ...
... L by recursion, so that the branch space of T is dense in L. L may have isolated points, but these are also open intervals, except for initial or final isolated points, which can conventionally be written as (∞, a) or (b, ∞), so we will also consider them to be open intervals. We form the 0’th level ...
For printing - Mathematical Sciences Publishers
... A corollary of these two theorems is that every power of a &pseudocompact space is pseudocompact. Now, it follows from Theorem 4 of [11], that any product of pseudocompact, locally compact spaces is pseudocompact, and that any product of pseudocompact, first countable spaces is pseudocompact. Since ...
... A corollary of these two theorems is that every power of a &pseudocompact space is pseudocompact. Now, it follows from Theorem 4 of [11], that any product of pseudocompact, locally compact spaces is pseudocompact, and that any product of pseudocompact, first countable spaces is pseudocompact. Since ...
TOPOLOGICAL GROUPS The purpose of these notes
... that x is contained in the interior of U . That is, U is not necessarily open, but there is an open set W ⊂ X containing x such that W ⊂ U . If G is a group, and S and T are subsets of G, we let ST and S −1 denote ST = {st | s ∈ S, t ∈ T } and S −1 = {s−1 | s ∈ S}. The subset S is called symmetric i ...
... that x is contained in the interior of U . That is, U is not necessarily open, but there is an open set W ⊂ X containing x such that W ⊂ U . If G is a group, and S and T are subsets of G, we let ST and S −1 denote ST = {st | s ∈ S, t ∈ T } and S −1 = {s−1 | s ∈ S}. The subset S is called symmetric i ...
ON THE EXISTENCE OF UNIVERSAL COVERING SPACES FOR
... Proof. First we apply [CC, Theorem 5.1] which states that any free factor group of the fundamental group of a second countable, connected, locally path connected metric space has countable rank. Thus π(X) is countable. Let x0 be a point in X. Let U1 ⊇ U2 . . . be a countable local basis for X, and g ...
... Proof. First we apply [CC, Theorem 5.1] which states that any free factor group of the fundamental group of a second countable, connected, locally path connected metric space has countable rank. Thus π(X) is countable. Let x0 be a point in X. Let U1 ⊇ U2 . . . be a countable local basis for X, and g ...
