# Shant Danielian

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I'm a recent graduate with a BS in CE and Applied Math. I enjoy both practical engineering applications and the mathematical theory behind it. I'm continuing in graduate studies in applied math in hopes of further blending engineering applications with mathematical rigor. I also enjoy studying pure math for fun and have gained an interest in abstract algebra and topology.

# 44 Questions

 5 Prove that any homeomorphism $f:X\to Y$ establishes a bijection between the components of $X$ to the components of $Y$. 4 Show that $S^n\cong\mathbb{R}^n\cup\{\infty\}.$ 3 Show that $f:\mathbb{R}^2\to\mathbb{R}$ defined by $f(x,y)=x+y$ is continuous using open sets. 3 Show that continuity together with finite additivity of measure implies countable additivity of measure. 3 Let $f:\mathbb{R}\to\mathbb{R}$ be continuous. Prove that the image under $f$ of each interval is either a single point or an interval. (w/o IVT)

# 644 Reputation

 +3 Plotting symbolic function using symsum +5 How does one show a topological space is metrizable? Using text Intro. to Topo. by Mendelson +20 Show that $S^n\cong\mathbb{R}^n\cup\{\infty\}.$ +2 Sobolev Embedding (Case: p=N)

 2 Compact and Connected. 2 Trigonometric Functions. Definite Integrals 2 Basic Calculus Problems. 0 Show that $S^n\cong\mathbb{R}^n\cup\{\infty\}.$ 0 Show that the infinite intersection of nested non-empty closed subsets of a compact space is not empty

# 27 Tags

 4 calculus × 2 2 trigonometry 2 general-topology × 30 2 derivatives 2 compactness × 10 0 proof-verification × 19 2 integration × 3 0 proof-strategy × 18 2 functions × 2 0 notation × 5

# 2 Accounts

 Mathematics 644 rep 115 Stack Overflow 103 rep 3