Tagged Questions
1
vote
1answer
52 views
Equivalence relation homeomorphisms
Is said to be $X\approx Y$ ($X$ is homeomorphic to $Y$) iff exists a function $h: X \longrightarrow Y$ which is bijective and preserves open sets, this relationship is an equivalence relation on $Top$ ...
0
votes
1answer
29 views
Do nets have subsequence?
Let $(P,\leq)$ be a directed set. Is there a cofinal and increasing function
$\theta:\mathbb{N}\to P$.
if $P$ has any maximal elements it can be proved easily. So I suppose $(P,\leq)$ none of it's ...
9
votes
1answer
147 views
Can we extend the definition of a continuous function to binary relations?
Let $X,Y$ be topological spaces. A function $\phi:X\to Y$ is continuous iff for any open subset $A\subseteq Y,$ the preimage $\phi^{-1}(A)$ is open in $X.$ We could similarly define a relation ...
2
votes
0answers
136 views
How to describe all continuous maps from T to T'?
How to describe all continuous maps from $T'$ to $T$, where $T=\mathbb{R}$ with natural topology (base given by the intervals $(a,b)$ ), and $T'=\mathbb{R}$ with the topology with basis given ...
