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Jan
1
revised The graph of a continuous function from a space $X$ into a Hausdorff space $Y$ is closed in $X \times Y$
added 6 characters in body; edited title
Dec
31
revised Compact Hausdorff Spaces with pre-caliber $\aleph_1$ has caliber $\aleph_1$
phi is not the empty set, a is a weird variable for an ordinal
Dec
31
revised What is a first countable, limit compact space that is not sequentially compact?
added 87 characters in body
Dec
31
revised What is a first countable, limit compact space that is not sequentially compact?
added 62 characters in body
Dec
30
comment What is a first countable, limit compact space that is not sequentially compact?
@ZachStone This topology isn't too bad. It's sort of "half" the usual topology on $\mathbb {R} $, and can be used to characterise "lower semicontinuous functions".
Dec
30
revised What is a first countable, limit compact space that is not sequentially compact?
added 1263 characters in body
Dec
30
revised What is a first countable, limit compact space that is not sequentially compact?
added 89 characters in body
Dec
30
answered What is a first countable, limit compact space that is not sequentially compact?
Dec
29
comment Acceptable generic and non-circular definition of countable infinity?
Comments are not for extended discussion; this conversation has been moved to chat.
Dec
27
revised Gentle introduction to algebraic number theory
link to pdf not exactly kosher
Dec
26
comment The epsilon-delta definition of continuity
@MathematicsStudent1122 Also functions like $ f(x)= \frac{\sin (1/x)}{x}$ ($f(0)=0$) which takes the value $0=f(0) $ at points arbitrarily close to $x_0 = 0$.
Dec
25
revised “Nested independence” of $\mathsf{ZFC}$?
added 131 characters in body; edited tags; edited title
Dec
21
comment Let $X$ an infinite $T_1$ space, then exist some subspace homeomorphic to $(\Bbb N,\tau)$ where $\tau$ is discrete or cofinite
@DanielFischer Your comment is perhaps a bit pedantic. There is no claim that this is a Choiceless proof. Furthermore, if the exercise is to show that every infinite T₁ space has a subspace homeomoprhic to $\mathbb{N}$ with either the cofinite or discrete topology, then we have to assume that every infinite set has a countably infinite subset (i.e., there are no infinite Dedekind finite sets, which is somewhat weaker than the Axiom of Countable Choice).
Dec
21
revised Compact sets in the lower topology on $\mathbb{R}$ have a minimum
no more sequence.
Dec
20
revised Compact sets in the lower topology on $\mathbb{R}$ have a minimum
spelling things out in excruciating detail
Dec
20
comment Is it consistent that every set is the countable union of sets with smaller cardinality, or is it just alephs?
@Wojowu: Part of it states, $N_G \models \text{'every set is a countable union of sets of smaller cardinality'}$.
Dec
20
comment Is it consistent that every set is the countable union of sets with smaller cardinality, or is it just alephs?
Then go further to Theorem 6.3 (p.86).
Dec
20
comment Is it consistent that every set is the countable union of sets with smaller cardinality, or is it just alephs?
Look at the statement of Theorem II.
Dec
20
revised Can a point and a compact set in a Tychonoff space be separated by a continuous function into an arbitrary finite dimension Lie group?
deleted 96 characters in body; edited title
Dec
20
comment $A$ be a subset of $[0,1]$ with non-empty interior ; then is it true that $\mathbb Q+A=\mathbb R$?
I think you are confusing the sum $+$ (i.e., $A+B = \{ a+b : a \in A, b \in B \}$) with the union $\cup$.