Is there any intuition for continuous embeddings?
Jan 1, 2026 · Let X, Y X, Y be topological spaces and X ⊂ Y X ⊂ Y. X X is said to be continuously embedded in Y Y if the inclusion map i: X → Y i: X → Y, x ↦ x x ↦ x, is continuous. The definition …
Continuous vs Discrete Variables - Mathematics Stack Exchange
Dec 14, 2025 · Both discrete and continuous variables generally do have changing values—and a discrete variable can vary continuously with time. I am quite aware that discrete variables are those …
Property of continuous functions regarding maximum
x is not continuous at x = ±π 2 x = ± π 2 and claim 2 as you point out is not necessarily true, f f can have discontinuity at a point and still have maxima and minima in its domain of definition.
Integral of non-continuous function - Mathematics Stack Exchange
Oct 28, 2024 · Integral of non-continuous function Ask Question Asked 1 year, 3 months ago Modified 1 year, 3 months ago
Is the projection function in a normed space continuous?
Dec 26, 2025 · Let (X, n) (X, n) be normed space and B B a basis (by basis I mean a set of vector such that every vector in X can be expressed in an essentially unique way as a finite linear combination of …
Show that the spectral radius is an upper semi-continuous function
Show that the spectral radius is an upper semi-continuous function Ask Question Asked 13 years, 4 months ago Modified 9 years, 9 months ago
Does there exist an unbounded function that is uniformly continuous?
I know that $1/x$ is unbounded on $ (0,5)$ (for example) and that since it is unbounded, it is not uniformly continuous. Does a function have to be bounded to be uniformly continuous?
uniform continuity - Holder continuous functions embedded in …
Holder continuous functions embedded in Sobolev Ask Question Asked 10 years, 9 months ago Modified 5 years, 8 months ago
general topology - Continuous selection from an upper hemicontinuity ...
Nov 17, 2024 · Roughly, UHC correspondences admit approximations, i.e. continuous selections of the epsilon-enlargement of the graph, whereas LHC correspondences are better behaved for getting …
A short proof that if $f$ is continuous then $f^ {-1}$ continuous
Nov 9, 2024 · I learned a theorem that if $f$ is continuous and bijective then $f^ {-1}$ is continuous. I went online to search for a proof and saw a really long proof in this link.