Category:Weak Parallel Line Topology
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This category contains results about Weak Parallel Line Topology.
Let $\BB$ be the set of sets of the form:
| \(\ds \map U {a, b}\) | \(=\) | \(\ds \set {\paren {x, 0}: a < x \le b} \cup \set {\paren {x, 1}: a < x \le b}\) | ||||||||||||
| \(\ds \map W {a, b}\) | \(=\) | \(\ds \set {\paren {x, 0}: a < x < b} \cup \set {\paren {x, 1}: a \le x < b}\) |
that is:
- the left half-open real intervals on $B$ together with the interior of their projection onto $A$
and:
- the right half-open real intervals on $A$ together with the interior of their projection onto $B$.
$\BB$ is then taken to be the basis for a topology $\tau$ on $S$.
Thus $\tau$ is referred to as the weak parallel line topology.
The topological space $T = \struct {S, \tau}$ is referred to as the weak parallel line space.
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