# Tagged Questions

**6**

votes

**1**answer

221 views

### On the cardinality of perfect spaces with the countable chain condition

QUESTION: Does every regular perfect space with the countable chain condition have cardinality bounded above by the continuum? Is this at least true for perfectly normal ccc spaces?
Recall that a ...

**3**

votes

**1**answer

334 views

### On One point Lindeloffication of topological spaces

As you Know when we define a topological space to be the one point compactification of the topological space $X$, we look for a compact space $Y$ such that $X\subset Y$ and $X$ is dense in $Y$ and ...

**6**

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**4**answers

503 views

### On Pseudo-finite topological spaces

We recall that a topological space $(X,\tau)$ is Pseudo-finite, if each compact subset of $X$ is finite.
One of the classical example of Pseudo-finite topological spaces can be considered as an ...

**0**

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**1**answer

244 views

### Lindelöf subsets of $P$-spaces

A completely regular topological space $(X,\tau)$ is called a $P$-space, if every $G_\delta$-subset of $X$ is open .$\($i.e $\tau$ is closed under countable intersection$\)$. Here we recall some ...

**2**

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**0**answers

60 views

### Characterizing local homeomorphisms into an exponent

Let $X$,$Y$, and $Z$ be (compactly generated) spaces. Suppose $f:Z \to Y^X$ is a local homeomorphism. How can we tell this from its adjoint $\tilde f:Z \times X \to Y$? I.e., I want a property $P$ ...