Math 450 – Final 2025/2026 Exam
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100% Correct Answers
Connected - 🧠 ANSWER ✔✔If there is no disjoint nonempty open set U,V
separation of X, such that their unions equal X
Compact - 🧠 ANSWER ✔✔If every open covering of A of X contains a finite
subcollection that covers X
Path Connected - 🧠 ANSWER ✔✔If every pair of points of X can be joined
by a path in X.
Path - 🧠 ANSWER ✔✔A path in X from x to y is a continuous map f:[a,b] ->
X such that f(a) = x and f(b)=y
Sequentially compact - 🧠 ANSWER ✔✔A set K is sequentially compact if
every sequence in K has a subsequence that converges to a limit that is
also in K
First countable - 🧠 ANSWER ✔✔A space that has a countable basis at
each of its points
COPYRIGHT©NINJANERD 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER: 619652435. TERMS OF USE. PRIVACY 1
STATEMENT. ALL RIGHTS RESERVED
, Second countable - 🧠 ANSWER ✔✔If a space X has a countable basis for
its topology
Metrizable - 🧠 ANSWER ✔✔X is said to be metrizable if there exists a
metric d on the set X that induces the topology of X
T1 space - 🧠 ANSWER ✔✔If for two points x,y in X that there exists open
nbhds U, V such that x in U and y in V but both are not in the other
Examples of t1 spaces? - 🧠 ANSWER ✔✔Cofinite and Indiscrete
T2 Space - 🧠 ANSWER ✔✔Hausdorff - same as t1 but U,V are disjoint
Example of T2 spaces and their properties? - 🧠 ANSWER ✔✔R with the K-
topology
-Not compact
-Not path connected
-Not locally path connected
-Not metrizable
-Connected
COPYRIGHT©NINJANERD 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER: 619652435. TERMS OF USE. PRIVACY 2
STATEMENT. ALL RIGHTS RESERVED
Questions and Detailed Answers | Get it
100% Correct Answers
Connected - 🧠 ANSWER ✔✔If there is no disjoint nonempty open set U,V
separation of X, such that their unions equal X
Compact - 🧠 ANSWER ✔✔If every open covering of A of X contains a finite
subcollection that covers X
Path Connected - 🧠 ANSWER ✔✔If every pair of points of X can be joined
by a path in X.
Path - 🧠 ANSWER ✔✔A path in X from x to y is a continuous map f:[a,b] ->
X such that f(a) = x and f(b)=y
Sequentially compact - 🧠 ANSWER ✔✔A set K is sequentially compact if
every sequence in K has a subsequence that converges to a limit that is
also in K
First countable - 🧠 ANSWER ✔✔A space that has a countable basis at
each of its points
COPYRIGHT©NINJANERD 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER: 619652435. TERMS OF USE. PRIVACY 1
STATEMENT. ALL RIGHTS RESERVED
, Second countable - 🧠 ANSWER ✔✔If a space X has a countable basis for
its topology
Metrizable - 🧠 ANSWER ✔✔X is said to be metrizable if there exists a
metric d on the set X that induces the topology of X
T1 space - 🧠 ANSWER ✔✔If for two points x,y in X that there exists open
nbhds U, V such that x in U and y in V but both are not in the other
Examples of t1 spaces? - 🧠 ANSWER ✔✔Cofinite and Indiscrete
T2 Space - 🧠 ANSWER ✔✔Hausdorff - same as t1 but U,V are disjoint
Example of T2 spaces and their properties? - 🧠 ANSWER ✔✔R with the K-
topology
-Not compact
-Not path connected
-Not locally path connected
-Not metrizable
-Connected
COPYRIGHT©NINJANERD 2025/2026. YEAR PUBLISHED 2025. COMPANY REGISTRATION NUMBER: 619652435. TERMS OF USE. PRIVACY 2
STATEMENT. ALL RIGHTS RESERVED
