2026 ELITE CERTIFICATION PROTOCOL
General Topology Mastery Practice Test 2026 | Exam Prep
Timed mock exams, detailed analytics, and practice drills for General Topology Mastery.
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Q1Domain Verified
Consider a topological space $(X, \mathcal{T})$. If a subset $A \subseteq X$ is a $G_\delta$ set, what can be definitively stated about its complement $A^c$?
$A^c$ must be both a $G_\delta$ and an $F_\sigma$ set.
$A^c$ must be an $F_\sigma$ set.
There is no general topological property that can be definitively assigned to $A^c$ based solely on $A$ being a $G_\delta$ set.
$A^c$ must be a $G_\delta$ set.
Q2Domain Verified
Let $f: X \to Y$ be a continuous map between topological spaces $X$ and $Y$. Which of the following statements is *always* true regarding the preimage $f^{-1}(V)$ of an open set $V \subseteq Y$?
$f^{-1}(V)$ is open in $X$ if and only if $f$ is a homeomorphism.
$f^{-1}(V)$ is always closed in $X$.
$f^{-1}(V)$ is always open in $X$.
$f^{-1}(V)$ is open in $X$ if and only if $V$ is open in $Y$.
Q3Domain Verified
In a topological space $X$, let $x \in X$. If $\{U_\alpha\}_{\alpha \in I}$ is an open cover of $X$, what is the significance of the statement that $x$ belongs to the interior of $\bigcup_{\alpha \in I} U_\alpha$?
It implies that $x$ belongs to the intersection of all $U_\alpha$.
It implies that $x$ belongs to at least one of the open sets $U_\alpha$.
It implies that $x$ is an isolated point of $X$.
It implies that $x$ is a limit point of $X$.
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This domain protocol is rigorously covered in our 2026 Elite Framework. Every mock reflects direct alignment with the official assessment criteria to eliminate performance gaps.
This domain protocol is rigorously covered in our 2026 Elite Framework. Every mock reflects direct alignment with the official assessment criteria to eliminate performance gaps.
This domain protocol is rigorously covered in our 2026 Elite Framework. Every mock reflects direct alignment with the official assessment criteria to eliminate performance gaps.
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