Skip to content

Commit ee8fdc1

Browse files
yhx-12243prabau
andauthored
Apply suggestions from code review
Co-authored-by: Patrick Rabau <70125716+prabau@users.noreply.github.com>
1 parent bbde466 commit ee8fdc1

File tree

2 files changed

+4
-3
lines changed

2 files changed

+4
-3
lines changed

properties/P000227.md

Lines changed: 3 additions & 2 deletions
Original file line numberDiff line numberDiff line change
@@ -9,8 +9,9 @@ $X$ has a discrete closed subset of cardinality $\mathfrak c=2^{\aleph_0}$.
99

1010
*Note*: This property implies $e(X)\ge\mathfrak c$,
1111
where the *extent* $e(X)$ is the supremum of the cardinality of discrete closed subsets in $X$.
12-
But there are spaces with $e(X)=\mathfrak c$ and without discrete closed subset of cardinality $\mathfrak c$,
13-
i.e., where the supremum is not attained, under certain set-theoretical assumptions.
12+
But, under certain set-theoretic assumptions (for example, if $\mathfrak c=\aleph_{\omega_1}$),
13+
there are spaces with $e(X)=\mathfrak c$ and without discrete closed subset of cardinality $\mathfrak c$,
14+
i.e., where the supremum is not attained.
1415

1516
Compare with these properties, where $D$ denotes a discrete closed subset in $X$:
1617
- {P107} $(\exists D: |D|=1)$

spaces/S000009/properties/P000227.md

Lines changed: 1 addition & 1 deletion
Original file line numberDiff line numberDiff line change
@@ -4,4 +4,4 @@ property: P000227
44
value: true
55
---
66

7-
Let $p$ be the particular point. $X\setminus\{p\}$ is an closed and discrete subspace of cardinality $\mathfrak c$.
7+
Let $p$ be the particular point. $X\setminus\{p\}$ is a closed and discrete subspace of cardinality $\mathfrak c$.

0 commit comments

Comments
 (0)