# Recent questions tagged spaces

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Compute the dimension and find bases for the following linear spaces.
Compute the dimension and find bases for the following linear spaces.Compute the dimension and find bases for the following linear spaces. a) Real anti-symmetric $4 \times 4$ matrices. b) Quartic polynomials $p$ wi ...
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When are bases in Euclidean vector spaces V (Rⁿ or Cⁿ) topologically stable?
When are bases in Euclidean vector spaces V (Rⁿ or Cⁿ) topologically stable?When are bases in Euclidean vector spaces V (Rⁿ or Cⁿ) &nbsp;topologically stable? ...
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Let $f: N \rightarrow Y$ be a function defined as
Let $f: N \rightarrow Y$ be a function defined asLet $f: N \rightarrow Y$ be a function defined as $f(x)=4 x+3$ where $Y=\{y \in N: y=4 x+3$ for some $x \in N\}$ Show that $f$ is invertible and its i ...
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Let $f:(-1,1) \rightarrow B$, be a function defined by $f(x)=\tan ^{-1} \frac{2 x}{1-x^{2}}$, then $f$ is both one-one and onto when $B$ is the interval.
Let $f:(-1,1) \rightarrow B$, be a function defined by $f(x)=\tan ^{-1} \frac{2 x}{1-x^{2}}$, then $f$ is both one-one and onto when $B$ is the interval.Let $f:(-1,1) \rightarrow B$, be a function defined by $f(x)=\tan ^{-1} \frac{2 x}{1-x^{2}}$, then $f$ is both one-one and onto when $B$ is the interv ...
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Let $A$ and $B$ be metric spaces, and let $f: A \rightarrow B$. Suppose that whenever $X$ is an open set in $B$, the set $\{a \in A: f(a) \notin X\}$ is closed in $A .$ Which of the following must be true?Let $A$ and $B$ be metric spaces, and let $f: A \rightarrow B$. Suppose that whenever $X$ is an open set in $B$, the set $\{a \in A: f(a) \notin X\}$ ...
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How do I quantify chance in Finite Sample Spaces with Equally Likely Outcomes?
How do I quantify chance in Finite Sample Spaces with Equally Likely Outcomes?How do I quantify chance in Finite Sample Spaces with Equally Likely Outcomes? ...
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Give examples of random statistical experiments and their sample spaces
Give examples of random statistical experiments and their sample spacesGive examples of random statistical experiments and their sample spaces ...
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Are all topological spaces metrizable?
Are all topological spaces metrizable?We say that a norm $|| \cdot ||$ generates a toplogy $\tau_{|| \cdot ||}$ if and only if $\tau_{|| \cdot ||}$ is the smallest tolpolgy in $X$ that con ...
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Does the Pythagorean theorem generalize to arbitrary inner product spaces?
Does the Pythagorean theorem generalize to arbitrary inner product spaces?Does the Pythagorean theorem generalize to arbitrary inner product spaces? ...
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What are normed spaces?
What are normed spaces?What are normed spaces? ...
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Vector spaces can contain other vector spaces. If $V$ is a vector space, then $S \subseteq V$ is said to be a subspace of $V$ if
Vector spaces can contain other vector spaces. If $V$ is a vector space, then $S \subseteq V$ is said to be a subspace of $V$ ifVector spaces can contain other vector spaces. If $V$ is a vector space, then $S \subseteq V$ is said to be a subspace of $V$ if ...
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What are vector spaces?
What are vector spaces?What are vector spaces? ...
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What is an event in probability?
What is an event in probability?What is an event in probability? ...
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In probability what is an event with respect to sample spaces?