diff --git a/properties/P000028.md b/properties/P000028.md index 115326524..2e305af90 100644 --- a/properties/P000028.md +++ b/properties/P000028.md @@ -4,6 +4,8 @@ name: First countable refs: - zb: "0386.54001" name: Counterexamples in Topology + - zb: "0684.54001" + name: General Topology (Engelking, 1989) --- A space with a countable local basis at every point. @@ -17,3 +19,4 @@ Defined on page 7 of {{zb:0386.54001}}. - A space that is locally {P28} (every point has a neighborhood with the property) has the property. - $X$ satisfies this property iff its Kolmogorov quotient $\text{Kol}(X)$ does. +- This property is preserved by countable products. (Corollary 2.3.14 in {{zb:0684.54001}}) diff --git a/spaces/S000054/properties/P000050.md b/spaces/S000054/properties/P000050.md deleted file mode 100644 index 2ac14ad7d..000000000 --- a/spaces/S000054/properties/P000050.md +++ /dev/null @@ -1,11 +0,0 @@ ---- -space: S000054 -property: P000050 -value: false -refs: -- zb: "0386.54001" - name: Counterexamples in Topology ---- - -Asserted in the General Reference Chart for space #62 in -{{zb:0386.54001}}. diff --git a/spaces/S000076/properties/P000028.md b/spaces/S000076/properties/P000028.md index b1eba8f17..b5fcb5df2 100644 --- a/spaces/S000076/properties/P000028.md +++ b/spaces/S000076/properties/P000028.md @@ -2,12 +2,6 @@ space: S000076 property: P000028 value: true -refs: -- zb: "0386.54001" - name: Counterexamples in Topology --- -$X$ is a product of first countable spaces. - -Asserted in the General Reference Chart for space #84 in -{{zb:0386.54001}}. +$X$ is the square of {S43} and {S43|P28}. diff --git a/spaces/S000076/properties/P000050.md b/spaces/S000076/properties/P000050.md index 31845f7ac..ba345f7ea 100644 --- a/spaces/S000076/properties/P000050.md +++ b/spaces/S000076/properties/P000050.md @@ -2,10 +2,6 @@ space: S000076 property: P000050 value: true -refs: -- zb: "0386.54001" - name: Counterexamples in Topology --- -Asserted in the General Reference Chart for space #84 in -{{zb:0386.54001}}. +$X$ is the square of {S43} and {S43|P50}. diff --git a/spaces/S000076/properties/P000065.md b/spaces/S000076/properties/P000065.md index ff5820e6d..aad39d8eb 100644 --- a/spaces/S000076/properties/P000065.md +++ b/spaces/S000076/properties/P000065.md @@ -2,10 +2,6 @@ space: S000076 property: P000065 value: true -refs: -- zb: "0386.54001" - name: Counterexamples in Topology --- -Asserted in the General Reference Chart for space #84 in -{{zb:0386.54001}}. +Since $\mathfrak{c} \cdot \mathfrak{c} = \mathfrak{c}$.